I wish I could recommend you some co-op games but my experience of them hasn't been great. Maybe it's my playstyle, but just charging ahead guns blazing doesn't really work for me and gaming - maybe I am playing them wrong though.
Obviously Borderlands is the daddy of co-op these days. You could also try Dead Island, which has a cheap GOTY edition now - I found it great fun but eventually it gets samey. All the combat is via melee in this, with some small shooty bits, so you are up close and personal with the zombies.
Another option would be Resi 5. I haven't played this in co-op yet though. Also the Left 4 Dead games. How come these all feature zombies?
AH! Hunted: The Demon's Forge got good reviews for co-op - and you get to play through as a Conan and Archer Chick I believe....might be ideal?
The big one for me is Portal 2, which I am still waiting for my co-op partner to buy and play through the single player. We are near the end of Borderlands 2 and kinda drifted away from Dead Island, but he has just got PS+ so I guess the free Resident Evil 5 is next