I'm a master at using religion, I would highly, highly, recommend you put fourth some

into play here. First off, hope they have a civic other than theocracy. Okay, let's say they do, worry not you can convert the non-believers.
First off you'll want to make sure *
YOUR OWN CIVIC* is off theocracy. If they don't have it adopted, it isn't a problem(so skip this step). In the case it is, however you must use the ways of those hot women spies to change their religious civic type to your own(which is why you must be off theocracy). This will cost

points, so plan ahead and build up a little before taking action.
Next, when the religious defenses are down, spam their cities with missionaries(have the max 3 waiting, keep 1 or 2 high production cities ready to produce them). You don't *
HAVE* to get all cities for the final step to work, but it is recommended to work quickly/steadly towards getting 90-100% of their controlled cities.
Lastly, the final thing to do

points wise, is to again go to a city of theirs with your religion present in it, and click something among the lines of convert religion(you'll know it when you see it, just can't remember at this very moment). Then finally it's done!
Ah, but not so fast. There is a catch of course! If you didn't get all those cities that religon(you so dearly claim is "the way"), it could end up being only a temporary political theater.. AI's are as stubborn as a 5 year old's when it comes to switching off their religion(Just like real life people!). The best thing to do to make it stick, is as said get mostly all, to all their cities covered, and improve relationship with them.
The relationship can take two paths. I'm struggling to keep it simple, basically you can force (vassel talk) them into it, and they will come to accept it. Or just be friendly towards the civ leader in a way you'd treat your own child(considering your own child can't kill you).
GOOD LUCK!

It does work out, persistence beats AI's stubborn resistance.
Final note: You better be working with a holy religion
YOU control/started, or you're completely wasting your time. Ouch!
