I love shmups and a lot of them have co-op capabilities, but sadly I have nobody to actually be my player 2 (wife refuses to touch shmups lol).
That said, I've been playing Guardian Force on the Sega Saturn lately. It's pretty okay overall, the interesting bit is that Player 1 and 2 actually have different weapons to each other. You can pick up different weapon types, but even if you pick up the same color weapon, you'll both have something different to bring to the table. Player 2 is a bit more defensive but weaker than P1. It's pretty interesting.