Rocket League (1-4 players)

Jackbox Party Pack 1+2 (3-8 Players each player needs phone/tablet/laptop)

Screencheat (1-4 players)

Borderlands Handsome Collection (1-4 Players)

Diablo 3 (1-4 Players)

Trackmania Turbo (1-4 Players Splitscreen, though this games much better with a full screen for each player)

N++ (1-4 players)

Rayman Legends (1-4 players)

Enter the Gungeon (1-2 players)

Minecraft (1-4 players)

Call of Duty BlackOps 3 (1-4 players)

Plants vs Zombies Garden Warfare (1-2 Players)

Lego Games (1-2 players)

Tetris Ultimate (1-4 Players)

Risk (1-4 players)

Trivial Pursuit Live (1-4 players)

Trials Fusion (1-4 players)

Worms Battlegrounds/WMD (1-4 players)


Coming Soon:

Distance

Redout

Grip

Everybody's Golf

Aside from others that have listed:

- Resident Evil 5-6 HD remaster
- Resident Evil Revelations 2
- Broforce <-- insanely stupidly fun if you enjoy 80s & 90s action movies
- Tricky Towers/Tetris
- Gaunlet
- Lara Croft and the temple of Osiris
- Dead Nation
- Helldivers
- Drawful 2 <-- So far this has been the party game at my place, its very simple you just use your smartphone device to draw and I've played with 8 of my friends locally. The game can get pretty dirty(+18) depending on what your friends like to draw xD Highly recommend it.

- LittleBigPlanet 3 is cool, specially playing community games.
- Lego Marvel or Lego Avengers. Actually, all Lego games have split screen. But these two have a great open world.
- Rocket League.
- Resogun
- Star Wars Battlefront. It had the original survival mode where you faced hordes of enemies, but now it has Skirmish, so you can play offline with a friend in a 40 player match with bots. It's actually pretty fun since you can become Vader, Palpatine, Luke, Solo, etc and just destroy a mass of bots.
- Knack. You can play the campaign in co-op.
- I didn't played it on PS4, but Zombi mode in CoD usually is pretty fun to play.
- Rayman Legends.

You can also resort to basically any fighting game:
- Mortal Kombat X, The King of Fighters XIV, Guilty Gear Xrd, Injustice.

That's a great list thanks! 

Obviously FIFA is the big couch co-op franchise.

The Call of Duty games have split-screen.

The Lego games

One Piece: Pirate Warriors

The Samurai Warriors/ Dynasty Warriors games.

Star Wars: Battlefront

Rocket League

RE: Revelations 2

She likes gears I think but I've never been a fan. She doesn't like halo so that's out. She does like resident evil though thanks to Resi 4 years ago on Wii. But they've all been pretty bad since then lol. We used to play a lot off DKTF, Rayman legends and MK8 etc but yeah nothing lately

Somebody else mentioned RER2. Not a great game but we had a lot of fun playing co-op.

Almost every sports and driving game should probably work if you enjoy those at all. And while I can't speak for the PS4 versions, Dynasty Warriors games and such (e.g. Warriors Orochi) can also be a ton of fun, if that's your cup of tea.

Most of them are indie games.

The best has to be Rocket League.

Yeah will look into that and the upcoming RE7 if that has co-op. I often go to the Xbox section to look for decent local co-op games for xone and am always dissapointed. Only reason we bought it was cos it was on sale during Black Friday with two controllers and 3 Games. Never even used the other controller lol. May sell it for a switch 👍😁