I'd like to get some DRM-Free games to bring with me in a flash drive and play on any of my friends' PCs when I visit them. I found Cuphead is being sold here so that's my first option. Do you recommend any other one? Multiplayer games that require two or more PCs to be played, like Quake and Terraria, are out of the formula.

I have not yet played it but the first two games in the Trine series are considered to be pretty great games and they have local co-op.

So only 1 pc then? In that case most games that allow for 2 on the same pc will be fighting games:
https://www.gog.com/mix/fighting_games
But I suppose that's not quite cooperative :P

Jazz 2 has a split-screen mode, and according to wikipedia cooperative multiplayer exists, presumably in split-screen mode as well.

The LEGO games are great.
Rayman too (but make sure controllers are connected before launching the game)

Star Control II

Edit: Sorry, I missed the "co-op" bit. Still, SC2 is great fun with two players.

Here are some:

Guacamelee! (both editions, I believe)
Crimzon Clover (possibly also Caladrius Blaze)
Shovel Knight (given a recent enough version; the game didn't originally have this feature)
Tyrian 2000 (though I don't know how easy/hard it is to set up)

You might want to see if any of these games interest you. In any case, the last game on this list shouldn't be too expensive, so you should be able to afford it.

Serious Sam The first encounter and the second encounter have splitscreen coop. It's awesome. So that would be my game to go when it has to be splitscreen.

Nine Parchments - ignore the negative reviews, they just wished for expanded Trine 3. It's short twin stick shooter with magic.

I absolutely agree with this.
Also, remember to turn on the friendly fire to create total chaos! XD

I;m winging this reply but I was looking thru this week's sale and noticed this may have a split screen mode:

https://www.gog.com/game/giana_sisters_twisted_dreams

Just wanted to throw it out there.

Never Alone is also a nice co-op platformer you might want to consider.

If you want something slower paced, you could look at the Civilization series and similar games. Many of those games support Hot Seat multiplayer, which allows you to play with just one computer, each player taking their turn at the computer, then getting up so the next player gets a turn.

Some of these games even have a "Cooperative Victory" option, if you really want to play co-op; just make an alliance with the other player when you get a chance.

(Do note that these games can take a while; in the late game, it can take quite a while for the other player to take their turn. Even the AI can take a while to act, though a faster CPU should mitigate this somewhat.)

Wow, thanks for the suggestions, guys. I'm adding some of them to my wishlist.

Even more chaos? :D No, i play those games without friendly fire, just want to shoot the baddys!^^

Friends can respawn infinite times, so me and my friend used to prank a lot.
BOOM! Shredded by a cannonball. I swear I was pointing the baddie, really! You ran in between!
Three seconds ago revenge was made with me "accidentally" falling down a bridge.
Then I "inadvertently" blocked the way near a moving press wall, and so on! XD