Hey there!

Some games that we played:

• Overcooked 1 & 2, save the world by cooking in absurd environments. Shouting inclusive. (It's really fun, I promise!)
• Ibb & Obb - a fun little puzzle game
• Guacamelee was fun too, but we never finished it.
• Battleblock Theater is nice too! But I'm not sure if it's possible to play on one machine. So if you both have computers this is definitely possible.
• Unravel Two - it's fun! We haven't finished it yet, but it's a cute (and a bit sad sometimes) jump & run / puzzle platformer
• A Way Out was great too, really great story, but it's not cozy.
• ... and I noticed a lot of people gave you already some good games, while I was searching my library. xD

What I haven't tried yet but want to in the future:

• Moving Out - it looks similar to Overcooked, so I hope it will be fun
• Spiritfarer

It Takes Two is a good one to play with a significant other.

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

Make sure to check the Nucleus Coop App if you haven't already!

https://nucleus-coop.github.io/

It turns games that don't have a native local coop mode into local coop by simulating a LAN and running two instances of the game communicating exclusively with each other. It works really well, especially if you have a multi-monitor setup.

I have played multiple games in local coop with my brother with this, including Elden Ring. It's been a blast.

My list of split screen or couch co op PC games:

Basketball classics

Castle crashers

Cuphead

A Hat in Time

Katanari damacy reroll

Lego games (marvel, LOTR, Indiana Jones, star wars are my top 4)

Overcooked

Portal 2

Rocket League

Sonic All Star Racing Transformed

Spiritfarer

Strikey Sisters

Trine 2

Wingspan

And emulator roms for 2 players:

Secret of Mana

Zombies Ate my Neighbors

Game show games (family feud, wheel of fortune, you don't know jack)

I've heard nothing but good about Lovers in a Dangerous Spacetime. Haven't played it myself.

I was a bit confused when you said local co-op. It implies 2 computers on the same local network(connected to the same router, no internet connection required). I think the term you're looking for is split screen gaming.

When I looked at pictures of Spelunky games like Clonk and Liero popped into mind, I think there are options for split screen multiplayer in those games, they're old school PvP games.

I wouldn't recommend A Hat in Time, the local co-op is really bad because of how the camera works. :(

A few steam games I know:

ibb & obb
Dinasty Warriors 8

We played on PS but also available for pc:
It Takes Two
Stardew Valley
Children of Morta
Divinity: Original Sin 2
Cuphead
Guacamelee
Moon Hunters
Out of Space

Would you and your BF enjoy shooting at alien scum while your characters scream DEMOCRACY!! and HAVE A NICE CUP OF LIBERTEA!! at the top of their lungs? Would you be entertained by accidentally killing each other in the heat of battle when you radio for an ammo drop?

Then Helldivers would be for you. Join the forces of Super Earth and spread Managed Democracy throughout the universe!

PROTIP: If you want to assert dominance in your relationship, find a gun with a bayonet attachment. You will mix up the melee and interact buttons on at least one occasion.

It Takes Two is brilliant!

Magicka - top-down mage play where you can combine spells with each other (two beams make a stronger beam, etc), and friendly fire if you want to occasionally nudge or troll each other

Trine - side-scroller in 3D graphics with 3 unique characters; some platforming, action, and slight puzzles, and a very good story presentation/direction

Wingspan is a very solid port of the board game.

Since Wingspan is on there, why not put tabletop simulator on there too? It has got pretty much the same set of features in regards to multiplayer.

On that note, both of these games also have a "pass controller around" feature as well.

Heavenly Bodies

Recently picked up PlateUp, can definitely recommend that one as well. It's like a roguelike Overcooked. If your relationship survives this surely you can handle it all

Stardew Valley! Great split screen coop!

They've already been mentioned, but the two greatest games I've played with my SO is "It takes two" and "Unraveled 2". Please do yourselves a favor and play those!

If you don't mind something more casual and relaxing, Spiritfarer is good too. Wife and I played it in about a week. Very touching story at parts too.

I can recommend Lego Lord of the Rings. Me and my gf had a lot of fun, and it is the only Lego game I played with her that didn't bore me to death.

We tried Lego Harry Potter, and while she loves it (she loves the Lego games), I just found it boring as hell, so it depends on the person

The local co-op version of Untitled Goose Game is hillarious, highly recommended

Not real co-op, but my wife and I have played hundreds of hours of Wildermyth. Its an rpg with generative elements. We love reading out the lines of the characters in terrible accents. The battlr system is turn based so you've plenty of time to discuss what to do next.

Bombsquad available here:- https://tools.ballistica.net/downloads

Remember if you're a PC gamer, emulation is a great place to look for couch co-op since PC gaming seems to be rather averse to split screen unfortunately. There are a lot of extremely good split-screen games on PS2/GC that will look and run significantly nicer on PC.

It takes two is probably one of the best split screen local co-op imo.

My wife and I really loved these two that almost no one talks about since they haven't been around for long:
Rogue Heroes: Ruins of Tasos (co-op Legend of Zelda!)
Sun Haven (similar to Stardew valley)

Unravel (So touching, made me cry)
Project Zomboid (One of my fav games. I've played this split screen with my son. He kills the zombies, I organise the base)
A Way Out (Prison escape story)
Pinball FX3 (A classic two player experience)
Stardew Valley (Crafting/farming)
Beyond Two Souls (Story)
Skullgirls (2D Anime platform fighter)

It takes two, unravel two, a way out

We cycle between Plate Up!, Unrailed, and Helldivers in my household :) Other people have already mentioned them, but big +1 on all 3.

Stardew Valley!!

Gang Beasts is ludicrous fun! Flailing around, grabbing your little clayboy opponent and yeeting them off the side of a lighthouse will never not be fun. Definitely best played with a controller, though.

Dariusburst Chronicle Saviors is one of my favorites. It's a horizontally scrolling shmup with massive bosses and multiple routes. It has ultrawide support too.
The DLC is single-player only, so if you just want co-op, just get the base game

If you want a diablo-esque ARPG check out Ghostlore. It has some really cool mechanics with the glyphs, skill grid, and food. Oddly enough, the only multiplayer it supports is local co-op.

Edit: It should be noted that I haven't tried the co-op yet and after looking at the steam page again there's a review saying that it's buggy, so take this recommendation with caution.

Roots of Patcha is a fun, and some might argue, better alternative to Stardew Valley.

Many PC games support online co-op but have no splitscreen support. For a lot of these you can use a mod to run two instances at the same time and play them in splitscreen. Here's a link to the supported games: https://hub.splitscreen.me/