Local co-op games for 2 players

Binding of Isaac: Rebirth.

Lovers in a Dangerous Spacetime

Gang Beasts
Crawl (best for 4, but it works great for 2 also) - my favorite local co-op
Castle Crashers - some classic

Portal 2 (make splitscreen)

Guacamelee

Portal 2 is pretty fun in co-op if you want to solve puzzles together. EDIT: Unfortunately, I think you need to play a bit with the files to enable splitscreen.
I remember having a blast playing Rayman Origins with friends.
And Battleblock Theater. I only played singleplayer, but I heard it works just as great (if not better) for 2 players. And

Lego games are perfect for local coop

Any of the worms games if you like bashing each other's teams (and no hard feelings). It can be fun, especially if you play just for the lulz.

Orcs Must Die 2

broforce
castle crashers
helldivers
renegade ops

Goat simulator
8Bit Fiesta
Octodad: Dadliest Catch

Lego games.

trine tine2 trine3 l4d portal 2

We played a lot of Battleblock Theatre.
Chariot is somewhat fun, but gets boring, cause levels are long.
Broforce is good.
LEGO games - she loves them, but I don't((.
Magicka
Crypt of The Necrodancer
Spelunky
Lovers in a Dangerous Space-Time
Rocket League split-screen

Serious Sam 3 on 2 monitors with ultra panoramic resolution and vertical split screen. Also it supports multiple keyboards and mouses so its not like only 1 person can play on K+M and others need to play on gamepad

Monaco (1-4 players).

Divinity: Original Sin - Enhanced Edition

Brazzers : Tale of Two Sons
Sorry,it's Brothers, but I wanted to type a Bad Joke of the hour(BJ of the hour is another Bad Joke(bj))
You can blacklist me for such things
I have a nice pyramide here
But I prefer whitelists
Or asianlists
excuse me
or not

sonic all star transformers

Dungeon Defenders!

Rampage Knights

I think it depends a loton what games you prefer:

• If you like pain and torture and 2D pixel platformers then 1001 Spikes may be an idea or JumpJet Rex as it is far easier
• If you are interested in 2D beat them/shoot them up there are games like FistPuncher, Devil's Dare, Dead Pixels or Phantom Breaker
• A horror game? Then you could try Obscure
• Local co-op puzzle games are rarer but Shadow Puppeteer would be an example for that

There are a lot more. Also some where you have an additional co-op mode since the campaign is only single player.

Guacamelee, if she's kinda competent. But really, any game can become a couch co-op fun with your girlfriend.

Mortal Kombat X, any WORMS game, Serious Sam 3, FIFA, Rayman Origins, CoD: BO3