RetroGaming

R.C. Pro Am

Lemmings for Amiga had a 2player split screen mode. Goal is to guide the most lemmings (yours and the other players) into your exit.

SNES:

• Harvest Moon - this can lead into allowing the kid to plant something IRL and having them water it regularly, allowing them to "be a real farmer". Incidentally this is also a great way to get a child to eat vegetables, as a child who refuses to even consider eating a vegetable will change their mind when they grew it themselves

• Super Mario Kart

Mega Drive:

• Dr Robotnik's Mean Bean Machine - simple puzzle game with humorous characters from the old cartoon

The NES sesame Street games are pretty good.

My youngest loved sesame Street countdown. it was really forgiving and taught her basic platformer mechanics.

Pong

It doesn't count as non-violent, but every kid I have played it with has thoroughly enjoyed the TMNT arcade game (as well as the Simpsons game that plays similarly. If you play with them you can essentially carry them through the game and they are just along for the ride, but feel like they are part of the team.

A bunch of arcade games become much more friendly to kids with infinite continues, shmups, fighters, brawlers, etc but for those you'll need to filter on violence. I'd probably also avoid anything RPG or story heavy.

My picks would be Bubble bobble, Kirby on SNES, ice hockey on NES, Mario 1-3, super Mario kart, Tetris, monkey ball, Dr Mario. For Sega Sonic 1-3 & knuckles, ecco, robotnik's mean bean machine, Alex kidd, outrun

Joust. Easily understood game for little ones, and you can discourage player killing.

A c64 emulator? Then basically anything, LOCO maybe?

Kirby Super Star

That's easy. Daggerfall.

Lots of other great suggestions. But I do think the consensus is multiplayer games with coop.

Konami beat ‘em ups like TMNT, The Simpson, Xmen would be great.

I’m also going to throw in Party games or kart racers, CTR and Mario Kart of Mario Party or Crash Bash would also be great

That said Pokémon might be a nice option too though not sure how you’d play that together.

Or edutainment like Gizmos and Gadgets or Jumpstart

Sonic 2.

Controlling Tails can be good fun if you’re very young and don’t fully know what you’re doing!

Can be hard keeping both characters on screen at times though.

Super Mario World, Battletoads

Bubble Bobble is one of my favourite retro multiplayer games since it has both players playing simultaneously (not each take a turn/hand off the controller) but might still be a bit difficult for a 5 year old 🤔

Edit: Tetris & Dr. Mario for the SNES might also work

Sonic 2. Make him be tails. As is tradition.

Hard to beat Super Mario Brothers. I tried other classics, bunch of arcade games, but my son never liked them. Ms. Pac-Man might work. The big hit with us was Wii sports.

TMNT Turtles in Time on SNES. Its a fun game and kids can button mash, and turtles are still relevant today. Puzzle games like tetris can be good for using the brain. There were a ton of puzzle games in the snes era, like bust a move (puzzle bobble), yoshi's cookie, puyo puyo (kirby's avalanche), and many more.

I would mostly avoid NES because it looks really dated, aside from a handful of the real classics like Super Mario Bros 1 & 3.

Kirby Superstar (SNES) is great for this, I play it with my 5-year-old. The second player plays as the "helper" character, and when they die, Kirby can create them again. It effectively plays like a "buddy mode." That game is also one of my all-time favorites just for what it is, so I'm a bit biased.

Goof Troop, for SNES.

"Toejam and Earl: Panic on Funkotron" (Genesis) has a very well designed "little kid mode" in the options, and it's still really fun.

Edit: Example regarding violence - you get to throw jars at humans to trap them for transport back to earth. And you need to watch out for bowling balls falling out of trees.

You both can play Goof Troop. It's a Co-op game with Goofy and Max as protagonists, it's very funny.

Magical Quest 2 & 3 are very good for that. They already know the characters, and the games are beautiful and pretty good gameplay-wise.

You play together and if the child loses all his/her lives, he/she can steal yours. For difficult sections or bosses, you can do it alone.

There are new costumes regularly so the child wants to continue to discover the next costume, and its associated powers.

Magical Quest 2 is easier than 3, so I think it’s better to start with this one. You can either play as Mickey or Minnie.

In Magical Quest 3, you can either play as Mickey or Donald. Donald is meant to be played by the child because his gameplay is a bit different (with his soldier costume which is wooden barrel, preventing him to sink while Mickey has a silver armor which kills him if he goes into water with it). It’s not that difficult to play as Mickey (my nephew did not want to play as Donald and we had no major issues).

from a sega childhood my top:

• toejam and earl
• micro machines
• world of illusion (mickey and donald)
• California games
• Bonanza Brothers (has guns but in game they are tranquilizers and enemies wake up)

Balloon Fight (NES)

Sonic the Hedgehog 2. Little one can be Tails and play coop.

Oh, and sorry for so many responses, but I figure that posting these separately will let the votes give you some idea where to start.

The votes I've seen so far very much reflect the order I would try these games out with a five year old gamer.

Battle City

World of Illusion (Genesis)