@VadisDeProfundis (sorry for pinging, but it is a rather interesting thread)
Well, first and foremost, we need to consider the overall situation : for starters, is it the same 1967?
If yes, then there are certain problems. The King had supposedly promised the US ambassador that there would be no intervention before the elections. This is a bit self - defeating however, because, as general Kondylis (the man who restored the monarchy in Greece in 1935) allegedly said, you can organise a coup on any day of the year - except for the day after an election. Thus, it would be unfeasible for a government backed by the King and his generals to survive if the three "Apostasia" governments of 1965-1966 are offering a hint, without hard measures, and I am not very sure whether the generals would be ready -or willing- to crack the whip. Also, a large part of the initial success of the coup of the colonels came from the fact that most people expected the
Royalist coup, and that the colonels came out of nowhere for them. We don't know whether a generals' coup would be met with the same apathy or inactivity.
Also, the colonels could certainly have been arrested-in fact, there were many other instances, far more serious perhaps, where they could have been discharged; but there were many more low- and medium - rank officers that were sufficiently hard right - wingers to take their place (the "deep state" was a reality in 1949-1974 Greece). Thus, in my view, you would just see a different set of names toppling the government on a different day of the year, if nothing else changed. I believe that, for a general's junta, some more, not necessarily dramatic, changes are needed.
Part 1: the making of the coup (1951-1967)
The coup of 1951 is not very well known, because news of it were suppressed (for obvious reasons). But there is something interesting: there is a story that Papagos (the man whose bid to become Prime Minister caused the whole story of the 1951 coup) saw Demetrios Ioannides (the infamous later head of the Military Police and the "Invisible Dictator") in the courtyard of the Defence Ministry and that he approached him and asked him to drop his gun and stand down. Now, suppose that Ioannides, alarmed by the shouting civilian (allegedly Papagos was in civilian clothes) shoots at the direction of the voice. The bullet hits Papagos, who is badly, but not mortally wounded.
Now the future colonels are in deep trouble, since Papagos was a highly respected former general and the leader of the Right. A large part of the "respectable" Right is horrified when they learn what happened - "one of them" had been shot by a lowly army officer. Papagos, once having sufficiently recovered, pushes for the punishment of the seditious officers. Politicians, members of the court, businessmen press the King and the generals to look into the affair and find those responsible. The Americans, worried at the prospect of trouble in Greece just two years after the end of the Civil War and with the war in Korea still raging on, also want decisive action to prevent anything like that from happening again (after all, they wanted Papagos to become Prime Minister exactly because they considered his predecessor, Nikolaos Plasteras (another former general) too lax on communism). King Paul and his generals, who didn't want to weaken their grip on the army by purging its more radical elements but were also worried about this event and under pressure from so many different quarters, agree to launch an official investigation. In the end, Demetrios Ioannides and those that accompanied him in his operation to capture the Defence Ministry are court-martialled and sentenced to death for sedition. The rest of the officers, including Papadopoulos, are black-marked.
In the immediate aftermath of the coup attempt, not much changes compared to OTL: Papagos still becomes Prime Minister and is even more popular because of his stance in the whole affair and his personal plight. He will likely push for some ore controls on the military in the 1952 constitution, influenced by his experiences and he will probably try to undermine the remnants of IDEA (the dominant military faction since the days of the government-in-exile in the Second World War) inside the army, in order to prevent something similar from happening in the future; but apart from that, not much is different. Karamanlis is also very likely to succeed him as Prime Minister, since he had the support of the Palace and most likely, the Americans. But there are some differences: the government and the military leadership, fearful of a possible repetition of the events of 1951 and a split in the Right, monitor the military far more closely. After a few years, Georgios Papadopoulos, who could still have got his post in the Intelligence Agency (because he was supported - if not picked- by its director, general Natsinas) - but wouldn't probably be able to develop his ties to the CIA due to the suspicions surrounding his potential involvement in the 1951 incident, starts his rumblings about the "need to save Greece" and his other activities. The intelligence report reaches the Prime Minister's office; but this time, Papadopoulos isn't able to turn the whole affair around and end up retaining his position and getting the Chief of Stuff dismissed on the charge of corruption. Instead, he is swiftly discharged from the military , alongside many of his acquaintances in it, as the government wants to be more secure. Although this isn't the end of conspiratorial movements inside the army, the various potentate dictators are disorganised, divided and lacking any extensive connections with the various CIA agents in the country, while the Greek government and the Americans have a keen interest in keeping a tight leash on all these elements.
Enter the 1960s. Elections are bound to happen in 1960-1961 (unless something changes that). The populace is not very happy with the authoritarianism of the Karamanlis government, the scandals of that period and its handling of the matter of Cyprus. At the same time, the more limited (compared to OTL) crackdowns on the Left during the 1950s (due to the diversion of resources and the partial shift of priorities from these activities to keeping an eye on the military) and the bad taste 1951 left in the mouths of many in the moderate Right are projected to give the Centre Union * and the Left (United Democratic Left - EDA) an even larger percentage of the vote than OTL. Karamanlis, worried about this prospect, employs in turn an even more brutal form of the OTL Pericles Plan. The Hellenic Radical Union (ERE), his party, wins the elections, amidst widespread rumours of voter suppression and outright fraud. Georgios Papandreou, the leader of the Centre Union decides not to acknowledge the election results and launches a campaign to bring down the government. In the end, in 1963, Karamanlis is embarrassed by the assassination of some leftist politicians (for example Ilias Iliou and Christos Lambrakis) from far-right lone wolves (we could expect the likes of Gotzamanis - people who fled alongside the Germans in 1944, would have ITTTL a siege mentality due to the greater influence of the left and the suppression of the radical members of the military, that would push them to act even without the tolerance of the police/gendarmerie). Furthermore, he is very unpopular due to his seemingly servile behaviour vis-a-vis the Palace (we have no reason to assume that Frederica wouldn't be as hell-bound as OTL to running the country herself and getting her way with things like the dowry of princess Sophia or the funding of her charities-financial activities), his inability to hold the moderate Right with him and the distrust of the hard-right voters, while the Palace is on the verge of withdrawing its support. Thus, he is forced to resign. In the coming elections, Papandreou wins in a landslide and forms a government.
Georgios Papandreou encounters the same, or similar problems as OTL: the dispute with Turkey over Cyprus, the American pressure to mend this rift on the southern wing of NATO, domestic opposition from various groups to his reforms and dissent in his own party, largely caused by the meteoric rise of his son, Andreas Papandreou, who is considered to espouse radical ideas. However, with less threat from the military, he is actually able to push forward some of his policies, while the Palace is reluctant, for the same reason, to push things further. Thus, a sort of "cold peace" persists, while both sides build up their forces and the Palace begins to develop a new network of loyalists inside the military. However, the Prime Minister, feeling less pressured by the possibility of a coup, is able to continue his term.
Then comes the death of Paul in 1965. Papandreou believes that the new king, Constantine II, is more easy to work with, due to his youth. However, the young king is heavily under the influence of his mother, who in turn believes that she is in charge of the country and advises her son to adopt a confrontational stance. The first major clash between the king and the Prime Minister comes when the military leadership purges some officers suspected of being members of some "rather leftist" (in reality democratic - centre -left at most) officer clubs and organisations, which were allowed to grow considerably (in secret always), as the government's attention had turned to the right wing groups. Although Papandreou has no sympathy for the left, he senses this as an attempt to rebuild the reactionary networks that used to control the army and thus turn the military into an instrument to threaten the government; thus, he decides to fight the king over this issue, by assuming the Defence Ministry himself (as per OTL). The matter quickly becomes a hot topic, as there are allegations of certain senior government figures having relations to these leftist groups and that they planned a coup. The king demands that Papandreou step down immediately as Defence Minister and restore his former cabinet member that had this position to his post (this also happened OTL, but was not as outrageous as it sounds at the time, since the convention was that the King would nominate the Defence and Interior Ministers, to control the military and the Police and Papandreou himself had named a royalist as his defence minister). Papandreou refuses to obey the command, while daily demonstrations cause upheaval across the country. In the end however, Papandreou is toppled by an internal coup, as a number of his party's members of parliament side with the opposition (after much Palace and CIA prodding) in a contentious vote of no-confidence (the vote of the United Democratic Left, the leftist party, which supported the, government in the vote, were counted as "negative ones", due to the ideological orientation of their party) thus bringing down the government. The following days are characterised by anarchy, as the parliament is bickering over the no-confidence vote and the people demonstrate, enraged by the duplicity of the "rebel" parliamentarians.
The King, meanwhile, rushes to capitalise on this development, by naming his own government of members of the previous government that switched sides, expecting that the ERE would support it. This backfires however, as the Right is divided between those who want to support the new government and those who believe that such a move would be their political tombstone. Thus this first attempt fails. After another short-lived royalist government, which manages to win support from most of the ERE, but not enough to have a majority, the king agrees to form a final government that will organise elections in December 1966, on condition that any future government will have a defence minister appointed by the king , the elections will be based the law of proportional representation (which is disadvantageous to the Centre Union) and that the trials of the "leftist" officers will proceed. The major parties agree on these terms and back this third government. However, there is deep distrust between the King and the Papandreous, which is expected to create trouble again in the future.
Georgios and Andreas Papandreou seem to be polling high, something that worries many conservatives. The King is particularly anxious, as the Papandreous, particularly Andreas, campaign on the promise of far-reaching constitutional reforms that will limit the scope of the powers of the monarchy as they existed in the 1952 Constitution and will further increase civilian oversight of the military and democratize the country's institutions. However, he refrains - for the moment - from taking any action, as the ERE is also gaining strength, thanks to the leadership of Panagiotis Kanellopoulos, who is one of the few leaders of the party who are able to regain the moderate voters who begin to get uncomfortable with Andreas Papandreou's "socialist agitation". This shift is decisive, for it, combined with the electoral law, leads to a hung parliament on December 14, 1966. The country experiences unrest after this election, while the Centre Union continues to push for constitutional amendments inside a rather divided parliament. The instability inside the country alarms the military leadership and the Americans, who fear that the left may take advantage of the situation to present itself as an credible alternative to the two large parties. Thus, when the proposal of "a limited dictatorship" (a short period of martial law) under the supervision of the King and his generals, is presented, they are receptive to it as a way to restore stability and end the deadlock in government. The result is that, on January 23, 1967, a royal decree about the declaration of martial law across the country is announced.
* It is very possible that a party of the centre would be formed ITTL as well, as it was to the best interests of the Americans (who were instrumental to the formation of the OTL one): the lack of a strong centrist party allowed for polarisation, that benefitted the Right but also the Left. The presence of one, on the other hand, weakened the Right and the Left, reduced tensions and made the isolation of the latter more easy and durable. ITTL, there is even more motivation to weaken
both. As for the Papandreous, I think they were the only ones capable of leading such a disparate coalition of different groups as a single political organisation.
