If you have José María Gil-Robles and CEDA win the 1936 Parliamentary elections with a commanding lead you would see no military coup at all, instead you could see general unrest by anarchists and communists, with the military backing the Republic instead. You would end up with a right-wing Spanish Republic, bordering on fascist, and with some clashes against communists and anarchists rather than a full scale civil war.
Another option would involve full Soviet backing for the Republic, getting directly involved in the conflict, but that would also mean massive purges on the Spanish Communists to better fit the Stalinist line peddled from Moscow. It would also result in mass murder of anarchists, moderates, right-wingers, and other political dissidents after the war's end, resulting in a Stalinist Spanish Republic.
Either way, the moderates end up in a complicated situation, the political climate was already very polarized.
Personally, I think that if you want to keep the Second Republic surviving, the best way to do that would be to have a look at the root causes and go for those first. And the reality is that Spain is so complex and polarized during the early decades of the 20th century that it would take a miracle to get the Republic to work out, short of going for a POD so close that would avoid the Civil War. Still, unlike a certain sea mammal it's not impossible - heck, Spain had the good chance of being neutral during both World Wars, so that helps out tremendously, and I think those were the best decisions before the Transition that Spain made.
You know what? Let me think about it. I have a couple other projects to work on (including getting an f**kin' job), but I'll see what I can come up with. Don't ask me to turn it into a full-fledged TL, though.