Fun Coop games to play casually with my SO?

Warframe.

Degrees of separation has been released February 14th and is highly recommended for couples co-op play.

oh completely forgot about unravel 2 , it's amazing

I play a lot of co-op games with my wife. Many of the ones we've had a lot of fun with have already been mentioned. Some I didn't see listed in the thread are:

Dying Light - It is a zombie game, something like Left 4 Dead series, Contagion or Killing Floor series. The big difference is the parkour elements, along with some RPG aspects. It is more hand 2 hand combat than gun play.

Dead Island & Dead Island Riptide - done by the same team that made Dying Light. Similar games but lack the parkour elements. My wife liked the island setting. It is bright and sunny, very different than your usual zombie games, so she was scared less.

Dead Effect 2 - zombie shooter / RPG on a space ship.

Of the games that were already mentioned, the ones my wife and I have the most fun with are the Borderlands series, L4D series, Vermintide, Grim Dawn and Torchlight 2.

having a SO

wtf I thought you were a gamer

Monster Hunter World is not bad (though I've heard 2 players are a bit at a disadvantage compared to a full party, as monsters don't scale well).
Left 4 Dead 2 is also good but you'll be screaming at the 2 AI team players most of the time.
Dying Light is pretty good and scales pretty well so I'd definitely recommend it.
Borderlands 1 and 2 are also great co-op games. Pre-sequel as well, it's more of the same (didn't like the story though).
Diablo III is a good choice too. Diablo II is even better, if you can adapt to older graphics.

Blood and Bacon if you're looking for a horde-mode FPS that's cheap, good and silly.

Saint's Row 3 and 4 are also fun to mess around with in co-op mode.

Warframe

https://store.steampowered.com/curator/588052-Co-Optimus/
https://store.steampowered.com/curator/32660802-Intro-Gaming-Significant-Other/

also can anyone recommend levelheads?

for anyone that will follow this later, Risk of rain 2 is amazing.
1 is good too.

https://www.steamgifts.com/discussion/H0laH/borderlands-the-handsome-collection-97-steam-store

At the discount steam is offering (around 97% off), it is a bargain for probably one of my favourite co-op online games of all time.

You will not be disappointed!

https://store.steampowered.com/app/345330/Eden_Rising/

fun, coop rpg+tower defense combo game. Free, but free game content limited, however, if you join ascendant edition server you have access to the full game so if you own it your SO can join and both of you can explore the full game.

Most of the negative reviews about no character customization and that only female character playable in the game, YET, developers said more customization and male character incoming.

Full edition not cheap, but I have a 3 copy giveaway running for it if you want (very low entry number so far, like 17% to win one copy right now), however, it invites only and the giveaway link is on my YT video about Eden Rising. If you liked the free edition and want to play more with your SO feel free to check my steam profile, you can find the video there more easily.

https://store.steampowered.com/app/493900/Dungeons_3/

This is another game I played and playing recently with a friend. It is fun, the narration just brilliant.

Not played other coops in last few months, some might still have coop function but these what I played, and Cuphead but that split screen coop and you not wanted that, not sure it is available for regular coop as I not owning it, I play it with friends at Sundays movie/bbq day.

I tend to think about coop a bit differently though here is a short list of ones I dont think were mentioned yet that might be enjoyable:
https://store.steampowered.com/app/644640/Band_of_Defenders/
https://store.steampowered.com/app/39800/Nation_Red/
https://store.steampowered.com/app/637650/FINAL_FANTASY_XV_WINDOWS_EDITION/
https://store.steampowered.com/app/543900/METAL_GEAR_SURVIVE/
https://store.steampowered.com/app/375230/Warhammer_40000_Eternal_Crusade/
https://store.steampowered.com/app/105600/Terraria/
https://store.steampowered.com/app/427520/Factorio/
https://store.steampowered.com/app/274190/Broforce/
https://store.steampowered.com/app/221380/Age_of_Empires_II_HD/
https://store.steampowered.com/app/200710/Torchlight_II/
https://store.steampowered.com/app/286160/Tabletop_Simulator/
https://store.steampowered.com/app/512900/Streets_of_Rogue/
https://store.steampowered.com/app/49600/Beat_Hazard/
https://store.steampowered.com/app/206420/Saints_Row_IV/
https://store.steampowered.com/app/291860/Pit_People/
https://store.steampowered.com/app/233980/UnEpic/
https://store.steampowered.com/app/252950/Rocket_League/
https://store.steampowered.com/app/394510/HELLDIVERS_A_New_Hell_Edition/
https://store.steampowered.com/app/20570/Warhammer_40000_Dawn_of_War_II_Chaos_Rising/

Free games:
https://store.steampowered.com/app/230410/Warframe/
https://store.steampowered.com/app/304050/Trove/
https://store.steampowered.com/app/489520/Minion_Masters/
https://store.steampowered.com/app/386360/SMITE/
https://store.steampowered.com/app/444090/Paladins/
https://store.steampowered.com/app/570/Dota_2/
https://store.steampowered.com/app/238960/Path_of_Exile/
https://store.steampowered.com/app/440/Team_Fortress_2/
https://store.steampowered.com/app/563560/Alien_Swarm_Reactive_Drop/
https://store.steampowered.com/app/225840/Sven_Coop/

I tried to include a little bit of everything, since I am no mind reader of what you might enjoy; but in my humble opinion these are at least worth a look.

My top local coop is The Binding of Isaac - endless gameplay
Second one is the Rayman Legends / Origins

I don't think this was listed, but I recommend Towers Unite. It's fun :P

https://store.steampowered.com/app/204360/Castle_Crashers/

Stardew Valley

titan quest is fun, if you're into that. haven't tried it with my so, though.

Dream of Mirror is great for a MMO to play with just a couple people. You can literally do anything in the game solo aside from guild raids, so playing together works quite well. If you can get past the cell shaded graphics, that is.

Saint's Row 2 and 3 are a lot of fun with co-op. Not a big fan of 4 myself, but it would work too.

Orion Prelude is fun, you can set up a private game for just the 2 of you or have an open game for anyone to join. That's one game where if you're playing co-op the more the better.

I've enjoyed Unloved.

Dead Island
Sniper Elite 4 i think has coop
Dead Space 3
Borderlands 1, 2, presequel
Red Alert 3
Double Dragon Neon
No More Room In Hell
Streets of Rage 1, 2, 3,
Golden Axe 1, 2, 3
Saints Row 2 and The Third
Portal 2
The Forest
7 Days to Die
How To Survive 1 & 2
Magicka has co-op i think
Trine 1 and Trine 2 has co-op or maybe just 2, not sure
Enter the Gungeon has co-op i think, yeah, yeah it does, 2nd player plays as the Cultist, now i remember
Shank 2 has an co-op mode i think
Kane and Lynch Dead Men & Kane and Lynch 2 Dog Days
Broforce i think
Dead RIsing 2 & 3 i think too, avoid 4 tho
Worms Games, you could team up against others or AI
Helldivers
Mother Russia Bleeds
Warhammer Vermintide 2
Obscure games, all 3, maybe have co-op, maybe, yeah, yeah, 3 definetly

salt and sanctuary

They've been mentioned but:

Don't Starve Together
Overcooked 2
Divinity Original Sin 2

It would be easier to know what genre of games she likes.

I cannot help but recommend the amazing ' fortified' , it's so light and fun to