My other half isn't much of a gamer but she has my old low end laptop and wants a co-op game that we can play together. We've previously played Minecraft together but nothing else, she just wants something we can play together.
Any good recommendations that are cheap and not graphic intensive?
Okay, here is a good variety ones you can look into (since you say you have played Minecraft together, I'm assuming that these recommendations don't necessarily need to be couch co-op, and by 'not graphic intensive' you mostly mean a game that can run on a computer that can run Minecraft on low settings)
BattleBlock Theater (platformer)
Keep Talking and Nobody Explodes (bomb defusing)
Hammerwatch (series of hack'n'slash games)
Don't Starve Together (survival)
Risk of Rain 2 (rogue-lite)
I have also seen Overcooked, Terraria, Portal 2, and Stardew Valley have already been recommended. Those are solid ones as well
Monster Hunter may be too much for your computers, but if you would be interested in a similar game that is lighter weight, you could look into God Eater (1 & 2 are bundled together)
Also, if you end up having any interest in branching out into vs games, you could look into Crawl, SpeedRunners, Screencheat, Ulimate Chicken Horse, and Lethal League
Battleblock Theater reminded me of Castle Crashers from the same dev so I'll add that to this list. Fun platformy beat em up game that I played through with friends some 10 years ago.