Pixeljunk Monsters HD

This would be a perect choice because it's a non-verbal game that is easy enough to quickly get the hang of even for a 6 year old. On casual difficulty, it's a very easy game to beat and in co-op mode it's going to be a lot less boring than in singleplayer. It's a tower defense game without a speed-up button so in singleplayer there are moments when the game is tediously slow, this won't be a problem in co-op as you can talk to your kid while you both dance underneath towers to upgrade them, or one of you can walk around the map to collect coins and gems while the other one upgrades towers. It can be an addictive game, with soothing music and cute graphics. My main gripe is that there is no way to anticipate the creep pathing, making this game more about trial and error than a serious strategic challenge but if you play with a 6 year old, that's OK I guess.

PS: Plays perfectly with XBOX 360 controllers on a laptop

Fight the Dragon, if you don't mind Steam. It's got a local split-screen coop mode. I never tried it myself though. It also allows you to build your own levels from blocks, Lego or Minecraft style, in case that's something you or the six year old would enjoy.

I'll add to all suggestions already made:
Lara Croft and the Guardian of Light

I played it with my 12 year old nephew on local coop a few times. It's an action and puzzle game.
I have it on Steam but I believe it is also on XBox live.
However it has some animated violence so maybe you'll see it as not suitable to a 6 years old.

I recall 'Octodad' being a really fun local co-op game and it's here on GoG. Just super silly fun trying to work together to control an octop- I mean, a totally regular human dad who is not at all an octopus.

How's Divinity Original Sin for local coop? Does it lend itself more as a single player RPG or does it work brilliantly as coop?

As I understand, the Enhanced Edition works wonderfully for co-op. I'm not sure if the PC version has local co-op, but whether online or local, it's apparently a lot of fun! I'm sure you can find more info on the GoG store page, reviews and such.

Assuming that Larian ever manages to actually release Original Sin on Linux, that will be on the list for sure. I've owned it for a loooooong time, and haven't played it yet.

I guess not many people have played this one but its very fun and I highly recommend it.

Hoard - where you play as a Dragon and have to build the biggest pile of gold. Fight other Dragons, Knights that wan't to steal your hoard. Kidnap princesses, burn castles, cities, etc.

Vote for it: http://www.gog.com/wishlist/games/hoard

Sacred 1 and Sacred 2 if you're in for a grindy, casual ARPG. I'ts super fun.

If you check the GOG reviews for Hammerwatch, you'll see someone mention coopping it with a six-year-old. I've coopped it with my teenage little sister, and it's fun enough to solo as well.

We played about 30 minutes of ibb & obb the other night, and my son loves it! Some of the puzzles were a little convoluted for him to see, but he got right into figuring out each new obstacle. Nice that is largely noon-violent too.

If you're still looking for recommendations, Lovers in a Dangerous Spacetime looks like a neat local coop game but i never played it...

Oh, somehow i missed that recommendation on the first page. Uhm...

Well, you still have Relic Hunters Zero (free and cartoony) and Vertical Heroes HD (looks like a flash game but it's currently at $1 on Indie Gala Mixcellaneous).

A shame that Scribblenauts Unlimited doesn't have any kind of coop, i could see it being really great to play with a kid.

Great !  :-D