Wai Wai World 2 on Famicom emulator. Don’t need to know any Japanese to play and it has great cartoony sprites.

Bubble Bobble (NES) is great two player, though you’re competing

Buster Bros (PsOne, and probably others) probably one of my top 5 co-op games of all time

Micro Mages (retro despite being released in 2019 because it plays on original NES hardware) probably top co-op of all time for me

There’s quite a bit more but have various degrees of violence so won’t recommend those (Contra, Heavy Barrel, Silk Worm, Jackal, Life Force, etc)