I used to play a lot of beat 'em ups with my brother when I was younger, especially arcade and Sega Genesis/Mega Drive games. Sometimes we tried a shoot 'em up, but we were pretty bad.
For beat 'em ups, you can't go wrong with classics such as Double Dragon, River City Ransom and Battletoads, but these are older and honestly I played more 16-bit and up.
The Streets of Rage series and Golden Axe I and II for Sega Genesis are great.
For SNES, we used to play Rushing Beat - especially the last one, which is pretty weird.
I liked Sengoku 3 for arcade, and it's a very pretty game, but the hitboxes aren't super accurate.
Try the obvious choice Cadillacs and Dinosaurs, Dungeons and Dragons: Tower of Doom and its sequel Shadows over Mystara, Knights of the Round, Battle Circuit, and maybe Alien vs Predator.
I could even talk about 'deep cuts' such as Gaia Crusaders, but I'd stay here forever
very good picks. I noticed you left out Golden Axe's 3rd installment. gaming 'zines at the time panned it cuz of the plainer graphics n lame magic spell FX. well there's definitely a modicum of truth to both criticisms - however, the combat is superior. you can block. you can low-attack. you can do a special move to hit behind you (costs no life but is not invincible). in addition to this, the game is non-linear n you can pick alternate paths through the game. n 4 selectable chars with an unlockable 5th one - that play a bit more unique from each other whereas in Golden Axe 1 & 2, the 3 chars were not worlds away in how they played to say the least other than their magic prowess.
Streets of Rage 3 was also bein slammed at the time for Yuzo's experimental approach to the SoR/BK3 sdtrk. I remember as a teen being infuriated somewhat by their blatant tastelessness. closed-minded BS... but to each their own.
overall, file-index this post under as a 'jus sayin' xD
here's my picks: Super Double Dragon, Final Fight 3, Turtles in Time, Batman Returns, Contra III: The Alien Wars, Zombies Ate My Neighbors, Sunset Riders, Super Smash TV, [SNES],
TMNT II & III, Mighty Final Fight, Contra. Super C, Bad Dudes, OG Mario Bros, (not Super Mario), Urban Champion, Yie Ar Kung Fu, Karate Champ, X-Men (<--bwahaha kidding on the last one) [NES].
Ninja Gaiden,, Final Fight MD, Hyperstone Heist (meh), Contra: Hard Corps, Gunstar Heroes, Captain America & the Avengers, Two Crude Dudes, (hehe), Joe & Mac, Growl (c'mawn brvh it's the *day they freed the animuLz!!*), Altered Beast, Alien Storm, Spidey & Venom: Maximum Carnage & Separation Anxiety (just give em a shot they're not too shabby IMO) Bonanza Bros., Kabuki Fighter, DJ Boy (played this in the arcade too... strange n goofy lol), Ghostbusters, Rolling Thunder 2 & 3, Rainbow Islands, Ren & Stimpy's Invention, Snow Bros., Toejam & Earl & the sequel Panic on Funkotron, Forgotten Worlds, Gain Ground, Mercs, Viewpoint, X-Men (like with NES but this is a meh not a backfiring catastrophe of pure 8-bit horror) [Gen]
if a couple of these are actually single-player or they're more competitive than co-op I apologize.
n I can make such lists for other consoles if you name what you got or what you like to play on