well it depends what happens instead, I mean... funny story, in 1967 the CIA had set up for a General's coup, when the Colonels lunched theirs the Americans were pissed, thinking their Generals had lunched the coup with out telling them, before figuring out it was a totally different coup I'm guessing you don't mean "what if the Generals coup rather then the Colonels?"
With a 1960 POD.
Hmm, there's lots of events which, if played correctly, would be butterflied away - Lambrakis's peace march (where he was the sole runner), the Apostasia, and a few other things.
Ideally, however, unless I converse with the Greek AH.commers, I think 1960 is too late because the political scene by then is well and truly polarized. I would say an immediate post-Civil War POD would be better. If you insist on a POD in 1960, then give Konstantinos some backbone to stand up to Frederika and/or get Frederika out of the picture. Frederika is the main liability in the Greek royal family here, and her meddling into all sorts of affairs helped to sour the Greek public mood towards the royalty (as if the attitude towards the monarchy was already low and negative to begin with anyway). In fact, Frederika was the one who pushed the monarchy towards supporting the 1967 coup, in part because she basically ordered Konstantinos to "sign the bloody paper".
So I guess an immediate post-CW POD would be better.
For Frederika, would a convenient accident do it?
If she's out of the picture, how would Constantine react differently when the various political flashpoints come up?
It will affect the outcome of Greek language problem.
Sorry, what language problem are you talking about?
Katharevousa vs. demotic (Dimotiki)Sorry, what language problem are you talking about?
The struggle between Katharevousa and Dimotiki as the preferred standard dialect of Greek. Papandreou IIRC preferred Dimotiki, which was a vernacular, while the military preferred the elite dialect of the language.
Katharevousa vs. demotic (Dimotiki)