Lovers in a Dangerous Spacetime - here's a video of it.

Fight'N Rage if you want some beat'em up.

https://www.gog.com/game/trine_enchanted_edition
https://www.gog.com/game/trine_2_complete_story
https://www.gog.com/game/trine_3_the_artifacts_of_power
https://www.gog.com/game/jazz_jackrabbit_2_collection
https://www.gog.com/game/spelunky
https://www.gog.com/game/gauntlet_slayer_edition
All the LEGO games.

Super Puzzle Platformer Deluxe is also a good one.

Thank you for your ideas !

Here are some other games I found :
Liste des jeux coop qu'on m'a conseillés sur le forum de GOG, pour avoir vos avis, pour la chaîne CODE JPP :
SPELUNKY : https://www.gog.com/game/spelunky
ENTER THE GUNGEON : https://www.gog.com/game/enter_the_gungeon
OCTODAD : https://www.gog.com/game/octodad_dadliest_catch
LEGO STAR WARS : https://www.gog.com/game/lego_star_wars_the_complete_saga
BROFORCE : https://www.gog.com/game/broforce
TESLA VS LOVECRAFT : https://www.gog.com/game/tesla_vs_lovecraft
CRYPT OF THE NECRODANCER : https://www.gog.com/game/crypt_of_the_necrodancer
DIVINITY : https://www.gog.com/game/divinity_original_sin_enhanced_edition
SHOVEL KNIGHT : https://www.gog.com/game/shovel_knight
LOVERS IN A DANGEROUX SPACETIME : https://www.gog.com/game/lovers_in_a_dangerous_spacetime
PIXELJUNK MONSTERS : https://www.gog.com/game/pixeljunk_monsters_hd
GUACAMELEE : https://www.gog.com/game/guacamelee_super_turbo_championship_edition
TRINE : https://www.gog.com/game/trine_enchanted_edition
DEATH ROAD TO CANADA : https://www.gog.com/game/death_road_to_canada
WORMS : https://www.gog.com/game/worms_wmd
GAUNTLET : https://www.gog.com/game/gauntlet_slayer_edition

Good stuff on that list, played a lot of the original Spelunky, Worms, Guacamelee and Trine 1 and 2. Only played Worms (WWP and Armageddon) multiplayer thogh.
Another game that I'm not sure is considered co-op is "Brothers a tale of two sons". Is meant to play single player, controling the 2 brothers at the same time (kinda weird) but I played it with my GF and enjoyed very much. Simple and short but relaxing as well (compared to competitive or "hard" games), nice vibe and atmosphere.
Bought it cheap on steam, maybe one euro or two, good to spend 3 or 4 relaxed hours, like watching a movie.

Edit: isn´t shovel knight single player only?
Maybe the best way to check is to go to steam, search for co-op and look in GOG.

Crap, almost forgot don´t starve together...
I know you only wat GOG but Portal2 and Binding of isaac are great

The newest shovel knight updates makes the game co-op.

Overcooked is a great 4 player co-op game. A ton of hilarity and fun mechanics.

https://www.co-optimus.com/games.php

list of co-op games

DEATH ROAD TO CANADA is my favorite game so far !

Local co-op games me and my husband played together:
Guacamelee
Broforce
Mother Russia Bleeds
Death Road to Canada
Castle Crashers
Lovers in Dangerous Spacetime
Abyss Odyssey
Steredenn

Only finished Guacamelee, though. We're thinking of picking up A Way Out at some point. Our friends mentioned they had fun playing Monster Prom, but it looks to tumblresque for my taste. Divinity games and Brothers Tale of Two Sons are awesome, but I don't know how they play in local co-op.

If this game were on GOG, it would be the top answer, IMO. :)

Brothers is not meant to be played as a two player co-op game (and for good reasons!), but it's possible to pretend like it were and share the gamepad, and I think not few co-op players do it and enjoy playing it like that. I guess it's a matter of priority (experiencing the gameplay and story as intended or having fun with your co-op partner).

Anyway, I see noone has mentioned Overcooked and Overcooked 2 yet. Those are good co-op games, too, if you can warm up to this specific gameplay.

And apparently Victor Vran has local co-op as well. I haven't tested it myself, but you can check gameplay videos on YouTube.

RingRunner has a limited co-op option, though it's effectively a ship that lets one person steer and have a number of weapons while the second person can control a second set of weapons. Or one person can have a really big bulky ship and play it solo so it packs more punch... :) Alas that's the only couch Co-op it has.

All the Lego games (probably)

PixelJunk Shooters

Mortal Kombat series (MS-DOS, good luck getting it to play well with controllers)

Sacred 2 (360 & PS3 had a couch co-op... not sure about the PC version, might not)

Master of Orion 2 (Hotseat option)

Hi Pixlpixl!
In case you want pure co-op experience I would recommend Resident Evil 5 and 6 games. If you are up to fantasy strategies Heroes of Might & Magic is the best in my opinion.

Worms World Party & Worms Armageddon is some of the best local coop fun you can have. It is a very tactical, hectic, action packed and fun mix of a turn-based and real-time game. You can either ally up against the the computer played teams and play coop or you can do play competitively against your friends, all on the same computer.

https://www.gog.com/game/worms_world_party_remastered
https://www.gog.com/game/worms_armageddon

Heroes of Might and Magic 2 & 3 is also great fun with one or two other players if you like strategy games. It is not as time consuming as the Civilization and Age Of Wonder games. You do need several hours though to complete a game though.

The best choice you could do though would be to download an emulator and roms for one of the old 2D systems as they had a ton of cooperative games you could play on the same computer. There is also MAME for the vast forgotten wealth of arcade games, but that is a little more complicated to set up.