Contra honestly is one of the most fun games to play in co-op depending of the conditions (If it includes infinite continues by default, like the japanese Contra III, japanese Hard Corps and all versions of Rebirth, you can blitz it with persistence just like Cuphead), and if it doesn't...well, both will have to train a lot (NES Contra is probably the most entry-level despite everything) or simply use savestates.
Contra 4 is awesome but also tough as nails, and at least the emulator developers did say that they would look into that issue. Sure, I can play it with savestates already through it solo, but even if it takes many tries, beating it in co-op would be amazing.
And yep, it is great to be able to revisit (or for many, play for the first time) many DS multiplayer gems again. Its unfortunate that some games won't really work this way due to touch-screen only minigames/battle modes (Mario Party DS Zelda Phantom Hourglass were rife for chaos), but at least some of the best classics can be revisited in multiplayer now :)