can anyone recommend any local 2 player games from mine or my sons lists please (giveaway added)

No idea about most of them but the best local game I've ever played is Gang Beasts it'll be an amazing experience if u have controller
Ofc I haven't played local games a lot so only know few of them however I never forget that night me and my friends played it for the first time

ibb & obb
A Way Out
It Takes Two

Overcooked
Worms
Tricky Towers
Monaco

I only take a little look from the list but i see Castle Crasher and Overcooked already have a playtime. Other than that Portal 2 is great and i heard Rogue Heroes is fun.

From outside your list tho, me and my sister played Brothers - A Tale of Two Sons, Unravel 2, Rayman Legends awhile back and all are pretty fun.

For platformers, I enjoyed playing Guacamelee! and its sequel.

Glancing over your list of games, I've played these with my niece. Most of these are local coop, LAN or both. Some are only LAN:

The Adventures of Shuggy
Giana Sisters
Monaco
Move or Die
Never Alone
Nidhogg
Overcooked
Peggle
Portal 2
Ring Runner: Flight of the Sages
ROCKETSROCKETSROCKETS
Satellite Reign
Star Realms and Cthulu Realms
Stardew Valley
Trine / Trine 2
Torchlight 2
Worms (you have several of them)

Arcade Mayhem Juanito
Assault Android Cactus+
Fight'N Rage
Horizon Chase Turbo

Years ago I enjoyed Scott Pilgrim vs. The World on PS3 and now it's on PC, it has coop

Also adding Unravel Two to the list

Wizards of Legend
Plate Up!
Overcooked
Children of Morta
Nine Parchments

Those are just some of the games I have played with my sister where we had a lot of fun :)

Puyo Puyo Tetris
Brothers - A Tale of two sons
Armello
Degrees Of Separation

There were some discussions during the pandemic:
https://www.steamgifts.com/discussion/rI7J6/which-local-co-op-games-would-you-recommend
https://www.steamgifts.com/discussion/FHyGq/multiplayercoop-games-you-are-looking-for-pc
https://www.steamgifts.com/discussion/wWgnU/games-to-play-in-couple

https://store.steampowered.com/app/245170/Skullgirls_2nd_Encore/ might be worth a shot..
don´t know about local tho?!
https://store.steampowered.com/app/435150/Divinity_Original_Sin_2__Definitive_Edition/ looks great for together play
https://store.steampowered.com/app/791470/DYO/ for simpler pleasures + it´s FREE

giveaway added now - thanks for the suggestions

The Trine series is great in coop imho, I see justseedy has 1 and 2!

Also I had fun with Lara Croft and the Temple of Osiris :)

Some suggested Brothers - A Tale of two sons
That isn't a co-op game per se. It can be played with two people using one controller playing a thumbstick each of course.
And I wouldn't play that with a little kid. German Age Rating is 12 and that's about right IMO.
Also, is it couch co-op only or 2 separate PCs also?
Edit: Possibly Fall Guys, although multiplayer PvEvP focussed.

some of the best local couch games just in general:
platformers: ms splosion man, heave ho, broforce
puzzler: ibb and obb, shadow puppeteer, tiny brains
vs: gang beasts, samurai gunn, gun monkeys, rocket league

Castle Crasher, you can't go wrong with Castle Crasher. Human Fall Flat, Gang Beast is fun as well.

thanks everyone

What are their ages?

Kinda hard to filter co-op games on Steam like that. I'd suggest organizing your Steam library using Dynamic Collections and looking for local co-op, might miss a few games though.

If you sign here with your Steam account you might filter them easily.https://www.local-games.info/

Managed to filter them here: https://www.lorenzostanco.com/lab/steam/

mswigglenose/:
https://store.steampowered.com/app/557040/99Vidas/
https://store.steampowered.com/app/1454730/Chenso_Club/
https://store.steampowered.com/app/1004490/Tools_Up/

justseedy:
https://store.steampowered.com/app/253230/A_Hat_in_Time/
https://store.steampowered.com/app/2217420/AQUA_KITTY_UDX/
https://store.steampowered.com/app/617440/Arcade_Mayhem_Juanito/
https://store.steampowered.com/app/250110/Assault_Android_Cactus/
https://store.steampowered.com/app/618740/Beat_Hazard_2/
https://store.steampowered.com/app/452060/Caveblazers/ (might be too hard, but it's amazing)
https://store.steampowered.com/app/386620/Cook_Serve_Delicious_2/
https://store.steampowered.com/app/508790/Flat_Heroes/
https://store.steampowered.com/app/465200/Fury_Unleashed/
https://store.steampowered.com/app/842750/Galaxy_Champions_TV/
https://store.steampowered.com/app/534550/Guacamelee_2/
https://store.steampowered.com/app/477160/Human_Fall_Flat/
https://store.steampowered.com/app/747620/Joggernauts/
https://store.steampowered.com/app/252110/Lovers_in_a_Dangerous_Spacetime/
https://store.steampowered.com/app/113020/Monaco_Whats_Yours_Is_Mine/
https://store.steampowered.com/app/545270/NBA_Playgrounds/
https://store.steampowered.com/app/809870/Ninjin_Clash_of_Carrots/
https://store.steampowered.com/app/1107820/Pushy_and_Pully_in_Blockland/
https://store.steampowered.com/app/382490/Relic_Hunters_Zero_Remix/
https://store.steampowered.com/app/300380/Road_Redemption/
https://store.steampowered.com/app/1092630/Rogue_Glitch/
https://store.steampowered.com/app/787810/Rogue_Heroes_Ruins_of_Tasos/
https://store.steampowered.com/app/413150/Stardew_Valley/
https://store.steampowered.com/app/532190/Super_Blood_Hockey/
https://store.steampowered.com/app/396710/The_Adventure_Pals/
https://store.steampowered.com/app/350740/The_Bug_Butcher/
https://store.steampowered.com/app/416790/The_Metronomicon_Slay_The_Dance_Floor/
https://store.steampowered.com/app/516110/ToeJam__Earl_Back_in_the_Groove/
https://store.steampowered.com/app/704880/Tridents_Wake/
https://store.steampowered.com/app/35720/Trine_2_Complete_Story/
https://store.steampowered.com/app/566910/Zombie_Vikings_Stabathon/

I guess I'll also suggest random games!

Steam sale will come later this month, so wishlisting a few could be a nice idea.

Here's my playlist of local co-op games I've covered (396 videos for now), so all allow 2 (or more) players.
https://www.youtube.com/playlist?list=PLXSJgzsctNy046THcrVTAiF_XrnCoNPQ2

Subs are more than welcome!

Also have playlists by genre, but there will be some online co-op only games there as well:
https://www.youtube.com/@PoePra2/playlists?view=50&sort=dd&shelf_id=5

My 7 years old nephew really enjoyed playing these with me:
https://store.steampowered.com/app/238460/BattleBlock_Theater/ (nice platformer + puzzle combo)
https://store.steampowered.com/app/523660/HYPERCHARGE_Unboxed/ (FPS with some wave defense co-op)
https://store.steampowered.com/app/531510/Just_Shapes__Beats/ (nice rhythm action game)
https://store.steampowered.com/app/1016180/Terror_of_Hemasaurus/ (retro but modern rampage)
https://store.steampowered.com/app/1329500/SpiderHeck/ (has some wave survival in co-op, cool physics)
https://store.steampowered.com/app/1138850/Heavenly_Bodies/ (was hard for him but he loved it, he pretty much followed my lead)
https://store.steampowered.com/app/1071870/Biped/ (also had to lead most of the time, and once or twice had to pick his controller to go through some part)
https://store.steampowered.com/app/265930/Goat_Simulator/ (pure silly and fun game, we've aslo played the sequel, Goat SImulator 3, Epic exclusive)
https://store.steampowered.com/app/477160/Human_Fall_Flat/ (silly 3D platformer with goofy physics)

My personal picks:
https://store.steampowered.com/app/471550/Nine_Parchments/ (my favourite twin-stick shooter)
https://store.steampowered.com/app/914710/Cat_Quest_II/ (pure fun straightforward ARPG)
https://store.steampowered.com/app/336440/Super_Cane_Magic_ZERO__Legend_of_the_Cane_Cane/ (really goofy)
https://store.steampowered.com/app/996770/Moving_Out/ (my favourite overcooked-like)
https://store.steampowered.com/app/359840/Shift_Happens/ (platformer)
https://store.steampowered.com/app/374040/Portal_Knights/ (minecrafty)
https://store.steampowered.com/app/1253610/Knights_of_Braveland/ (roguelitey but very accessible beat'em up)
https://store.steampowered.com/app/822040/Super_Volley_Blast/ (one of my favourite sport games on steam)
https://store.steampowered.com/app/532190/Super_Blood_Hockey/ (maybe too violent for a child, but pure fun)
https://store.steampowered.com/app/598550/HUNTDOWN/ (classic run and gun, might be too hard depending on age, but it's a masterpiece)
https://store.steampowered.com/bundle/12294/Trine_Ultimate_Collection/ (franchise, any would work, amazing co-op game with puzzle, platforming and combat)

https://store.steampowered.com/app/701160/Kingdom_Two_Crowns/
https://store.steampowered.com/app/972660/_Spiritfarer_Farewell/
https://store.steampowered.com/app/887450/Tunche/
https://store.steampowered.com/app/985890/Streets_of_Rage_4/

https://store.steampowered.com/app/572890/Pikuniku/
https://store.steampowered.com/app/747620/Joggernauts/
https://store.steampowered.com/app/1306720/Mayhem_Brawler/

https://store.steampowered.com/app/880940/Pummel_Party/ 👍

https://store.steampowered.com/app/592480/Knights_And_Bikes

All of the Lego games are a lot of fun for local co-op! I used to play them with my dad as a kid and now still enjoy playing them and the newer ones with friends :) https://store.steampowered.com/app/214510/LEGO_The_Lord_of_the_Rings/ is great if you enjoy action, while https://store.steampowered.com/app/32330/LEGO_Indiana_Jones_The_Original_Adventures/ and https://store.steampowered.com/app/21130/LEGO_Harry_Potter_Years_14/ for example are a bit more puzzle heavy.

And if you're not that into Lego, you can never go wrong with Trine :) https://store.steampowered.com/app/35700/Trine_Enchanted_Edition/

Also the Metal Slug series
Guns, Gore and Cannoli series
Cuphead
Insane 2

lethal league blaze is great
man it sucks that codemaster removed their old racing games because race driver grid, grid 2, dirt 3 and grid autosport had all splitscreen
streets of fury ex
wee tanks
worms (3d ultimate or something like wmd or clan wars for 2d)
road redemtion
towerfall ascension
ultimate chicken horse