It might depend on the game. I'm not sure. But I just want to know in general which one is allowed.

Desume is the only decent one that I know of. It's been a while since I looked into it, but iirc, versions 0.9.10 and 0.9.11 are the two most commonly allowed since they are the most accurate.

Communities will usually allow DS emulators since the price of a DS capture card is expensive and can be hard to come by. Double check with the mods first too A ) make sure it's allowed B ) see if they have any recommended/required versions to use.

EDIT: when are we going to get emotes surrounded by colons so I can properly use B ) without a space and without it turning into sunglasses? OpieOP

B) I think desmume is THE only one, haven't seen another DS emulator other than the different versions of desmume, at least what comes with Retroarch on the 3ds

As people have mentioned, Desmume is your go-to emulator. It's worth remembering though that just because it's the best option doesn't mean it's particularly accurate. For accuracy purposes, shelling out for DS capture is still greatly preferred.