On the SNES, all of the games below have coop:

• Tiny Toons Wild and Wacky Sports - a collection of several silly minigames as some sort of tournament, with minimum scores that need to be reached. No direct violence between players, only cartoon shenanigans like falling down a cliff, snowballing after tripping while skiing, etc. (Maybe show the kid some of the old cartoons as well, if s/he enjoys, I’m sure the game will be more interesting to him/her)
• Super Bomberman - Might count as “violent”, since you’re bombing weird looking enemies, but it’s a formula that rarely gets old and plays great as co-op. Your kid might enjoy 3 and 4 the most, with the variety of mounts to be had (if your rpi can run NeoGeo games, Neo Bomberman is also a great choice)
• Top Gear - Racing game with one of the best soundtracks in the console. Top Gear 3000 goes to space and has plenty of options for upgrading your car.
• Secret of Mana - Might count as “violent”, especially as you start off with a sword and kill cute bunny-thing enemies. An action RPG that, once you get the 2nd character, it can be played with the 2nd controller. Drop-in/drop-out, so you can easily join and leave while your kid plays or vice versa. The same applies for Secret of Mana 2 (Seiken Densetsu 3)
• Magical Quest 2 and 3 - Disney games that are best when played cooperatively (the first lacks coop). Starts off easy enough and you get new costumes that give special powers, which help you out in the stages going forward. It’s “Disney violence” how you beat most enemies (jumping on their heads, spinning them against one another)
• Kirby Super Star and Dreamland 3 - Both allow for a second player to join in and help. Dreamland 3 has a very unique and cute looking style.
• International Super Star Soccer - If you’re into normal football (soccer), this is easily the best of its kind for the 16-bit era
• NBA Jam - Also available on the Mega Drive, dunno which version is better. BOOM SHAKA LAKA!!