Gunstar Heroes would be great and I would also say Dinosaurs for Hire for the Genesis, which is a surprisingly decent run' n gun in that and the Contra vein. Also seems right up Vinny and Dan's alley in terms of dinosaurs wearing sunglasses and Hawaiian shirts.
Also as a huge fan of the Final Fight/Streets of Rage style beat-em-up, I'm gonna say that style of game is not well suited to this format. Mostly because optimizing your run means relying on stun locking enemies, which is fine when you're playing but boring to watch objectively. Shoot em ups inherently aren't very fun to watch either in my opinion, despite both of the aforementioned genres taking a pretty big share of the old, hard co-op game selection.
Run 'n guns are probably the best suited to this series, as we've seen with the Contra games. The Rolling Thunder games might be good, as while they're technically run 'n gun they also basically play like Shinobi.
Two Crude Dudes (previously suggested) is a 2D beat em up like an Altered Beast. I would have thought before that these would be great games for this series, but now after the earth shattering revelation that there is barely any strategy whatsoever to Altered Beast (which nobody actually thought was a good game, but it was a huge flagship title for Sega and... I really thought there must have been something else to that eye ball boss, you know?) I'm starting to think such game will either be too easy or have very similar issues.