I play huge maps and find a diplomatic victory easier than domination. I think there are two types of diplo victories. The first is when you beat and vassal enough AIs to elect yourself diplo victor (I consider this a domination victory on these maps). The second is when you have several stronge AIs vote for you. The first is easy to figure out, just read any warfare related threads, the second is more tricky, and here are some suggestions
1) Leverage religion early but do not exclusively rely on it. Most AIs switch to FR and you will lose that benefit, but if you were a loyal friend even religious zealots will remember (Brennus is like this).
2) Find out who you UN foe will be. The one with the most population. Build that person up so they stay #1 but ar ehated by other AIs. Example, help in war and help them vassal an AI or 2. Just make sure it's not enough to win the UN vote.
3) Do not ignore those request for tribute or help, a little kindness early on helps alot later.
4) Know who to trust and who not to. You can forget Qin, Catherine, Alexander, Napolean being a reliable ally at the end. Also the war happy AIs (Shaka/Monty/Ghengis) make poor allies since they will declare easily on other AIs.
5) Leverage the favorite civics throughout the game. Heretary rule befriends alot of AIs and it worth keeping AIs happy rather than running US or rep. Also note alot of AIs have one of the religion civics as their favorite, so having the same religion can be a double boost.
6) Do not hesitate to go to war for an ally, you do not have to send troop.
7) Open borders judisciously. You do not want an immediate -4 you traded with our worse enemies.
8) Forget defensive pacts. Too often I have lost good friends because I inadvertantly declared war on them when they attacked another AI I had a pact with.