any good recommendations for story base co-op games?

SR3

trine?

System shock 2

There is a story in the co-op section of Portal 2

Are you looking for fun co-op or a great story? I know story-driven co-op games that have meh story but are extremely fun and vice versa.

Dead Island..
As far as I remember there IS a story for it..

Saints Row 3

Resident Evil 6. I recommend local coop.

Torchlight 2 does not have a great story, but it does have great co-op

Dungeon Siege 3 had a surprisingly good story, and I thought it was quite fun (this comes from someone who did not like DS 1 & 2)

The Lego games are more fun than they deserve to be.

I don't know if Baldur's Gate 1 has it, but BG 2 actually has a co-op mode. It is not great, but the story is at least good.

Sniper Elite Nazi Zombie Army actually has a story. It is not great, and the game is short, but if it is 75% off, it is a worthy purchase.

I would recommend that you avoid Saint's Row 2, unless you are willing to tweak quite a few things. Saint's Row 2 runs at different speeds depending on your computer, which causes issues in MP, as two players might end up playing the game at vastly different speeds. Also, it is a horrible port, even when you don't take that into account. SR 3 is better in this regard. It is still not a great port, but at least it is playable out of the box.

Dead Rising 2, excellent co-op and excellent replay value - I can't speak for how well ported the PC version is but I have a lot of love for the game on xbox :)