What's the best or most stable SNES emulator for PSP?

SNES9xTYL is the best snes emulator on PSP AFAIK and the PSP is noticeably better than the DS at emulation. You should be able to play most games smoothly on PSP but some games like Kirby Super Star won't play at full frame rate. If emulation exist on 3DS, it might be a good platform to play SNES games at full speed, same with PSP vita but I didn't check so I have no idea, I just know these 2 portables are significantly more performant than the PSP.

Also if you haven't make sure to overclock the PSP to 333mhz.

There's multiple versions of this emulator so trying different version might give different results. The latest version I've found date from 2018 but seems to be from a different author: https://github.com/esmjanus/snes9xTYL/tree/mecm/Release which has a build usable on PSP Vita.