Combating Enemy Religion in City-States

I’ve found the AI will avoid converting your cities (unless they’re really aggressive), but be more-than-happy to go after your allied city-states. This is unfortunate because influence with them decreases slower when they are following your religion.

Diplomatically, you can’t demand the AI stop converting cities of your religion until they’ve actually converted one of your cities. Even if they do convert one of your cities, you demand they stop, and they do so, they’ll still convert city-states following your religion.

Normally, there’s an AI between me and the heathens, and I’ll simply bribe one into DOW’ing the other and all the missionaries/prophets will get soaked up in the war. However, this particular game put only open ocean between us, and all those missionaries/prophets are free to float right over and convert my neighboring allies.

So the question is: How can I stop opposing AI from converting city-states following my religion without actually going to war?

Hm. The only idea I have is to do the same thing I do for my capital. I use my great generals and admirals from wars to create a human wall around the CS, preventing enemy missionary/prophet getting into range to convert.

For city states, it's simply only trying to spread your religion to those that have an active quest for free influence.. And you'll need Great Prophet to dislodge an existing one.
And then don't worry about them being switched back, in fact this can cause you to later get a quest to switch them back for more free influence.