I have been playing split screen co-op with my friend and we only have one more section to go but he only has about 7 guns compared to me having all of them because I played through the single player. My question is, will he ever unlock all of the guns, specifically the Five-Seven pistol? And if so, how?

You kind of answered you're own question: "... compared to me having all of them because I played through the single player."
He'll just have to play through the single player to get the rest of them.  And the Five-Seven pistol?  I'm pretty sure you have to get through the single-player campaign.

Not in the co-op campaign but if you guys play last stand he will. For the bigger guns anyway. Not pistols.

He can't play the single player because he doesn't have the game, we play split-screen. Thanks for your help, last stand it is

Couldn't you let him play the single player a bit to round out his guns then?  Throw it on Rookie and let him just run through it?