Looking for suggestions for games without violence

I haven't played it but some friends play and recommend Overcooked! 2.

Totaly Reliable Delivery Service this game maybe. I guess it's epic exclusive right now also epic gave it away during lunch period. If you collect those you can check if have it. Also epic link https://www.epicgames.com/store/tr/product/totally-reliable-delivery-service/home

I absolutely love Stardew Valley, but I guess it's the 'standard' recommendation for games with no combat.
Pikuniku has a multiplayer, and although I haven't played it yet, I don't think there's any violence in there? I've played part of the single player campaign and apart from slight spoiler breaking some eggs -which ends fine because the birds inside will live - and kicking a rock who likes it, it's got no violence so far and it's just some bouncing fun. Don't be misguided by the aesthetic, it provides plenty of challenge for adults too :).
There's always Jackbox Party Packs, but that might not be your thing?
I like Badland as a co-op game because while you and your clones can die, it's not graphic and it's good fun. There are no evil enemies or anything either, just you against the environment.
I hope one of these can help you get in the direction you're looking for, even if you pick something else :) good luck, hf!

Football Manager
Main Assembly
Oh...Sir!! The Insult Simulator
Pang Adventures
Sport games https://store.steampowered.com/search/?tags=701%2C3843

Can't go wrong with BattleBlock Theater.

Human Fall Flat
Farm Together
Worbital
We were Here Together/We were Here Too
Balloons TD 6

Games with no to little violence that come to mind:
Knights & Bikes
Kwaan
Stardew Valley
One Hour One Life
Overcooked series
Unravel Two
Heave Ho
Ultimate Chicken Horse
Monaco
Minecraft (or Creativerse on Steam)

Northgard

Oh, i play mostly violence games, so I am a bit desperate with my steam library. What about:

Some Civilization
Fishing simulators
Human flat fall (i haven't play that yet, so i expect it is not violence)

Well, i guess that is all i can add to discussion. Extra violence games would be longer list.

https://store.steampowered.com/app/620/Portal_2/

If you like sports/racing games at all, I can recommend these for online multiplayer:

Baseball -- Super Mega Baseball 2; Super Mega Baseball 3
Basketball -- NBA Playgrounds; NBA 2K Playgrounds 2
Golf -- The Golf Club 2; The Golf Club 2019
Mini-golf -- Golf With Your Friends
Kart racing -- Garfield Kart - Furious Racing; All-Star Fruit Racing; Sonic All Stars Racing Transformed

No violence and multiplayer/co-op?
if violence in real life is not a concern, go for FIFA or PES!
Though I suspect you have already played it.
Go for PORTAL 2,
Overcooked2,
Keep talking and Nobody explodes,
Human Fall flat,
or what above people recommended-Stardew valley
Really wish for MP in The Talos Principle (like portal2) but...wishes seldom come true

If you like co-op platformers then ibb and obb is pretty good, as far as "violence" goes I'm pretty sure then only thing you need to be wary of is spikes, same with Heave Ho.
Keep Talking and Nobody Explodes has no violence if you succeed on disarming the bomb in time.
You also have Ultimate Chicken Horse which also follows the "no violence, if you avoid the spikes".
Then there's my personal favourite, Uno.

A Hat in Time maybe? I mean, it does have fighting but the cartoonish kind. And its newest DLC adds a co-op mode.

Sonic & All-Stars Racing Transformed is... basically SEGA's Mario Kart. So a family friendly over the top racing game. It has a little bit of violence in its power-ups I guess... but at least there is no Blue Shell. XD

Kinda stretching the "No Violence" part but 100% Orange Juice is a pretty fun board game. Yes, there is fighting but, again, it's done in a cartoonish dice-determined no-real-consequence kind of way.

Minimal Violence: DemonCrawl

You might find these two threads interesting:

• Games you can't lose
• Can you recommend me any wholesome games? ♡

Train Valley 2

Been playing and loving it. Relaxing soundtrack and pretty challenging trying to get all 5 stars for every level.

Stardew Valley minus the caves doesn't have violence?

I guess things like Overcooked or Animal Crossing has no violence.

Overcooked 1&2

Keep Talking And Nobody Explodes (one of my favorites to play with friends)

Sonic All Stars Racing

If your friend is close to you, so you can play local coop, Crypt of The Necrodancer

I recommend Assault Android Cactus if you don't have it already
Also Cat Quest 2

I can recommend Factorio, it's a lot of fun to play in multiplayer and since the factory must always grow, there is always something to do.
You can play without the biters and have a violence free game (it's how I play most of the time too).

What about playing flippers ? there's some even free and you can share the pads : you take the right one, your friend the left one :D
There's city building sims also (cities skyline, sim city), and all simulators like bus sim, lumberjack sim, farmer sim, flight sim, etc. (but not all sims are multi/coop)

Tetris.