Here are some great co-op games I would recommend. I'm not sure what you and your friends game style preference is so I'll include a variety.

1. Borderlands 2 - great looter shooter, a ton of fun, good art style, and hilarious writing. This qould be my go to recommendation, I've got almost 100 hours in this game. If shooting and looting is your style then I'd say give Borderlands 2 a try. The game originally came out in 2012 so the min. system requirements should be easily attainable.

2. Portal 2 - This is probably the best puzzle game I know. Again a great game to play with a friend, the puzzles are extremely interesting and the writing is hilarious. Portal 2 is a lot shorter than the other games in this list, you should be able to get through it in 10-20 hours, so if you're looking for a shorter game and your into puzzle games, this is a fantastic game to check out.

3. Terraia/Minecraft - These are both crafting/sandbox games, I'm sure you're familiar with Minecraft. Terraia is very similar to Minecraft but it is 2D and takes a more adventure oriented approach to the sandbox genre of games. If you are into the sandbox crafting genre I'd suggest checking our Terraia, there's still a lot of support for this game and you can easily sink a ton of time into it with you're friends.

4. Rocket League - This game has become extremely popular as of late, it's essentially soccer with rocket cars. I don't think I can really adequately describe Rocket League to you so suffice it to say this game is stupidly fun and I'd recommend looking it up because it's crazy.

5. World of Warships - This game is made by the same devs that made World of Tanks. I just recently started playing this game and it's been suprisingly fun and it is pretty laid back. If floating around shooting massive canons is your style then I'd recommend checking out World of Warships. (This game is also F2P)

6. Warframe - To be honest I'm not sure this will be super helpful recommendation, but Warframe is a fantastic Destiny sytle F2P looter shooter that I would highly recommend to anyone. I'm not sure what the system requirements are but I imagine they are quite high since it is a particle intensive game. It is also a little hard to get into, but if you and your friends are looking for a game to really sink your teeth into, this would be it. It also supports more 2-4 player co-op.

Hope this helps. I'd love to hear your thoughts on any of these games if you end up trying one out :)