Oh okay, quite a few differences from the UN victory it seems. Guess there hasn't been a whole lot compiled on it because everyone sees it as such a cheesy victory. I did find some educational threads in the HoF forum though, from past religious gauntlets. Thanks for the info!
there is abundant literature on cheesy AP victories in the HoF subforum.
The trick obviously is to be in your target religion on the turn you finsih it and then never again, or possibly just between the vote and the counting ...
What you seem ignorant of and that is of higher value, is the way diplomacy goes.
Maybe I should write a "ways into diplo points"

.
Quick summary
bonus diplo moves
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peace, growing with turns (doesn't get big AFAIK, +2 max?)
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open borders, growing with turns (+1 after a while, max depends on the AI AFAIK)
- "
fair trade" (aka getting ripped of in a trade), max +4, grows with unfair trade benefitting the AI. gifting something to an AI you just met (= on the turn you meet him) gives you instant +4.
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same religion, growing with turns, can be big, depending on the AI (+7 for isa isn't rare)
- same
"favourite" civic, growing with turns, can be significant depending on the AI. you need to keep using the AIs favourite civic and he needs to be running it too. One of the easy ways to cheese your way to an AP win (because many AIs favour organized religion, which is easy to get early + beneficial while building a wonder).
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mutual struggle = bash the same dead horse. you can keep a war going for ages and grow this one quite high.
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giving help/tribute = give in to an AI's demand. if he was happy before, he'll be even happier, if he was angry before, he'll be less angry + won't declare for a while. It's not very big, but you also get the fair trade in the same time + it's sometimes easy.
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accepting favourite civic = agree to changing to an AI's favourite civic. same as giving help, it's not very big, but it's fast and also gives you the shared civics after a while.
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accepting a religion change = agree to changing to an AI's state religion. same as giving help, it's not very big, but it's fast and also gives you the shared religion after a while.
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providing resources = selling or gifting resources to an AI. grow with turns x number of resources. You can gift resources as soon as you have a trade network to an AI's capital. so this one is easy (you don't need most of the resources in the beginning) and early (no real prereqs, but having the wheel or sailing helps a lot). You can grow it faster by selling/gifting several resources.
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sharing technology = trading monopoly techs to an AI. Not all AIs care, but some do. Mansa Musa for instance.
I certainly missed some, but working those will net you enough diplo +s for a diplo win.
negative diplo moves
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war (duh!, do you really expect your war target to vote for you?)
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declaring war gives a flat -3 AFAIK, there may be a chance for the AI to forget every turn, but generally it's never forgotten.
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razing a city = you razed one of this AI's cities. flat -1 for each razed city AFAIK.
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razing a holy city = you razed a holy city, whatever the religion, whomever city it was. Bad idea.
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nuking = you nuked an AI and now you want his vote?
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declaring war on a friend = you declared on some other AI which this AI was pleased+ with. Flat -1, with a chance to forget, but don't count on it.
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trading with the worst enemy = this AI is angry with some other AI, and you traded with this AI. Big penalty (-4 ?) + he will ask you to stop trading, and you get another penalty if you don't give in.
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you brought an ally in a war against us = you bribed an AI to declare on this AI. small penalty, but it's almost never forgotten.
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you refused to help during wartime = the AI asked you to fight an enemy and you refused. too bad.
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you refused to give tribute = the angry AI asked for a tribute and you refused. -1 + he will often declare on you. (you can also refuse civics or religion, and get a penalty for those). Note that Gandhi asks 100 times in a game, but doesn't give penalty for a refusal.
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heathen : you have a religion, and it's not the right one. Grows with time, and gets big.
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vassals : for each vassal you have, you get a penalty.
getting the bonuses is hard enough, but if you start with penalties, you'll never make it.