Co-op recomendation

Unturned, Burnout Paradise, Screencheat, Borderlands (2/Pre-Sequel).

The Metal Slug games.

tried viscera cleanup detail yet?
pretty fun on coop i think :)

maybe wargame red dragon if u two wanna try RTS.
or Blazblue for fighting game :P
or Worms ultimate mayhem for turn based strategy (really funny)
Also 7 days to die if u wanna try surviving together, best survival on steam imo. u can turn off zombie if u just wanna survive the wild.

u two seem to love fps, i just suggested something a little different since u two seem to find fps too easy.

Trine.

helldivers
alien swarm (free)
borderlands
dead island
dying light

Borderlands games.
Rampage Knights.

I suggest Starbound if you like exploring and building stuff, Broforce if you like to destroy stuff, Trine games for nice puzzles and lovely environment.

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

Probably no ARPG's

Still can't resist and HAVE to suggest Grim Dawn, SadisticKitten will back me up on this one as I practically forced her to buy it and we played the ever living shit out of it. Fantastic game, sucks you in and is dripping with content.

Probably no ARPG's

Ok...
Football Manager - If you like Football, infinite game time for multiplayer.
Borderlands 1/2 - Great romp seeing as it seems you like shooters.
Civilisation V - Infinite gaming time again, gotta like strategy.
Rocket League - Sports game with a large community, again, probably infinite replayability.
Town of Salem - Great fun for a drop in, drop out blast, classic mafia/werewolf forum game. Free via browser as well as being on steam.

Don't Starve Together

saints row series or gta 5? there are plenty of things to do there.

Well i don't play co-op often, but i watched a gameplay video for vermintide today and found that pretty interesting.
It's a medieval/steampunkish L4D.

how about PAladin game in beta ?

Dead island, dead island riptide, alien swarm (free), left 4 dead or 2. Maybe I'll add some later if I will remember more.

From my library I can recommend you:

Broforce is a good game, but the online can be unstable. Not sure if they fixed those issues.
http://store.steampowered.com/app/274190

Serious Sam if you want a good brainless shooter. Get Serious Sam Classics: revolution to play the first and second encounter as a single game.
http://store.steampowered.com/app/227780/
Or maybe you can get the HD versions of those two games. Or the third one, it's good too:
http://store.steampowered.com/app/41070
I'll not recommend the second one because it's... weird. It's another Serious Sam, but the world feels a bit childish.

Castle Crashers if you want a beat'em up, the only negative point for me is that normal enemies have a LOT of health.
http://store.steampowered.com/app/204360

Don't Starve Together is some kind of survival game, fun to play with others, but first find some guide, I still don't have idea how to restore health after respawning.
http://store.steampowered.com/app/322330

Saints Row: The Third is like a GTA game but really crazy and unrealistic (in a good way). I finished the game with 3 different friends and we had a really good time.
http://store.steampowered.com/app/55230

Terraria is like Minecraft in 2D with a lot of weapons, enemies and decorations. You need to kill the bosses in order to invoke the last one.
http://store.steampowered.com/app/105600

You can play the Half Life 2 campaign in cooperative with Synergy, it ruins a bit the ambient while playing with someone else, but it's good to have a good time.
http://store.steampowered.com/app/17520

Unepic have a cooperative mode, but it's not the main campaign. I never tried it with friends, so I'm not sure if I must recommend it or not. The game itself is really good.
http://store.steampowered.com/app/233980/

Monaco: What's Yours Is Mine is a top view stealth game, I had a good laughs with this one.
http://store.steampowered.com/app/113020

Warframe is a free game, if you like space ninjas grinding games. I have 300 hours played.
http://store.steampowered.com/app/230410

Dead Island Definitive Edition and Dead Island: Riptide Definitive Edition (I own the old versions, but it's the same game). Kill zombies, craft your weapons and level up. The negative point for me is that the enemies don't have a level per zone, they always have YOUR level, a bit more or a bit less.
http://store.steampowered.com/app/383150/
http://store.steampowered.com/app/383180/

Mercenary Kings can be another option. I played it with my brother but... I don't know. It's not bad but at the same time I'm not sure if recommend it. Check it yourself:
http://store.steampowered.com/app/218820

I think that's all I can recommend from my library. If someone else want to recommend coop games based in the own library, check this web:
http://www.lorenzostanco.com/lab/steam/

(Sorry for the horrible format of my comment)

Brawlhalla. Free and fun game to play with your friends.

If you love Half-life 1 then Sven-Coop. Still loads of fun.

Sniper Elite 2 & 3
http://store.steampowered.com/app/63380/
http://store.steampowered.com/app/238090/

Rainbow Six Vegas 1-2, Splinter Cell: Chaos Theory and Conviction, Left 4 Dead (first one), Saints Row: The Third, Orcs Must Die! 2, The Lord of the Rings: War in the North, Trine 2, Pool Nation...

Orion Prelude and ORION are good fun.
They only cost 1,- each so could be worth a try.

No More Room in Hell is a free game which is amazing but very difficult.

Empyrion is probably very forgiving for lag since it's not an extremely active-combat type of game.

Lastly: Battleblock theater.

A list that I have with a friend (fast copy and paste, "Ya" means "game already beaten" )

Portal 2 - Ya
Minecraft - Ya
Trine 1 - Ya
Trine 2 - Ya
Trine 3 - Ya
Left 4 Dead 2 - Ya
Dawn of War: Last Stand - Ya
Killing Floor - Ya
Borderlands - Ya
Borderlands 2 - Ya
Borderlands The Pre-Sequel - Ya
Payday 2 - Ya
Saints Row 4 - Ya
Orcs Must Die! 2 - Ya
Factorio - Ya
Ibb & Obb - Ya
Battleblock Theater - Ya
Starbound - Ya
Terraria - Ya
Sniper Elite V2 - Ya
Sniper Elite V3 - Ya
Sanctum - Ya
Sanctum 2 - Ya
Dont Starve
Attack on Titan
Fifa 16
Alien Swarm
Far Cry 3
Battlefield 3
Sniper Elite V2 Nazi Zombie Army
Rainbow Six: Vegas 2
Supreme Commander
Monaco: What’s Yours is Mine
Arma III
SimCity

Magicka 1 and magicka 2

Terraria
Zombie Army Trilogy

If you're such hard-core gamers, you might consider Rainbow Six Siege. Its Standard Edition is sold again for 15€ on Uplay.
The main difference from the base game is that every new operator class costs about 10 times more renown (ingame currency).
More grinding but gives enough time to learn how to use each operator.