I'm not talking about bribing an AI to switch, I mean will they ever switch if they already have a state religion if more of their cities are a different religion?

I'm wondering because I have a game where I'm sury and Confucianism and huayna is Buddhism but as far as I can tell he has at least 4 cities already confucinist and I think at most he has 4 that are buddhism and he only has 7 cities total. When I try to bribe him he says he doesn't like me enough so I wonder if I spread my religion a bit more if he'll voluntarily switch even though he's best buds with the other budda followers, asoka and pacal.

I share my religion with ramesses and am a little worried about being a heathen except that the only real beast around is gilgamesh who went and founded toaism so he's basically the heathen now and hates asoka. So I think I'm safe but would like more of the confucinist block between me and him, and huayna can get feisty sometimes.

Depends on the quantity of cities that have a certain religion, and if they possess the holy city.

Count population, if there are more Confu citizens he should be willing to take the bribe. (He'll give you 'not enough of our people follow that fate' otherwise even if he likes you enough) If he didn't found that religion, he also might switch on its own at some point. I don't know the exact mechanics though, maybe it also depends on how widely Confu is spread to other civs.

I think he already has more confusinism cities, but maybe not more population than buddism. He didn't found budda and his reason for not switching when I bribe him is he doesn't like me enough.

Well, you have three options to get it:

1) get him to like you enough in some other way
2) spread it around and hope he'll do it himself
3) use spies to force him

Similar Question: Is there any reasonable way to get an AI to switch to another religion that you aren't already running (but want to).

I.E., AI and I are both Hindu but I want to become Buddhist and bring my AI friend along with me. If I switch first we don't get the shared-religion modifier and he won't like me enough even though if he switched he would.

Note: In this case he founded both religions AND had both religions in all his cities.

^No, it's not possible. You have to adopt the desired religion first to be able to ask somebody to join you.