It is at least theoretically possible to get your own country force-converted by an enemy. AIs can demand force-conversion and vassalizations, but they are pretty rare because of the warscore requirements. Usually long before an AI has the warscore for such things, it will demand a cheaper peace and just get a province or two.
So, DoW an enemy who can force-convert you, and lose 50 or so battles to them, so that you are at -50 warscore. Then let them capture your capital, but only your capital. (You can let them capture other provinces, but then they will demand those, which you probably don't want.) Oh, and be sure to use up all your money -- they'll want that, so may as well give them little as possible.
Needless to say, this sort of thing is of mostly theoretical interest, since it is very rare to lose only one's capital in a war. But there are some pagans who can at least possibly pull it off. Mostly not to Muslims, of course, but to Christians. I.e. the Maya are fairly likely to be able to DoW Spain (or just let Spain DoW them, which they are programmed to do anyway), then let Spain capture only their capital.