Hi all,

Looking for some new platformers for my kid and I to enjoy. We are using a Makey Makey to play the games on an HTPC running Lubuntu 14.04 LTS. So far we have the following under our belts.

Beatbuddy: Tale of the Guardians
Runner 2: Future Legend of Rhythm Alien
Closure
Dustforce DX
Incredipede
Joe Danger 2: The Movie
Metal Slug
Metal Slug 2
Metal Slug 3
Metal Slug X
Never Alone
Offspring Fling
Thomas Was Alone
Volgarr the Viking
VVVVVV

Must be

* 2D
* Platformer
* On Linux
* 2 buttons maximum (Makey Makey only has two buttons and arrow keys)

I can recommend Crystal Caves series. Its very old, but very funny and classic. Runs in Dosbox and available for purchase on GOG too. Also BioMenace, but its linear. While at it, also check Jazz Jackrabbit. Also linear but very nicely drawn. I think it also needs only two action buttons.

Syoban Action meats your criterion. Left and right to move, up to jump.

Just don't expect the game to be fair. (You'll see what I mean when you actually try playing the game.)

Broforce should work.
Also old DOS games may work as well.

Cave Story - I prefer +, but the original is (should be?) still freely available. Metroidvania.
Limbo - If your kid is very young / easily disturbed, forget about this one. Puzzle platformer.
Super Meat Boy - Platforming platformer.
Braid - Puzzle platformer.

This game tends to require precise movements, so depending on how you are controlling it, it might be difficult. In particular, you will often need to quickly press away from the wall while pressing a button to jump off it. Also, you may need to sometimes press the run button when doing this. In particular, if you are, for example, playing this game with your feet, it's not going to work.

(With that said, you do only need 2 buttons + arrows: one to run and one to jump.)

Seriously?
I think sometimes Briad and Super Meat Boy can get frustrating even for adults.

Sure, but there'll be at least one adult present, and sometimes kids are better than adults at video games. Also, it's not like VVVVVV or Volgarr or Dustforce are exactly casual, frustration-free experiences. Honestly, I can't finish the first level in Volgarr - compared to that, SMB and Braid are merciful in how they gradually increase difficulty.

I remember playing this with my dad a looong time ago, so I think it shall fit your purposes nicely. It runs on Linux with DOSBox without any issue.

You might also check some older DOSgames, like Bio Menace or Rick Dangerous. These are your typical sidescrolling jumping and shooting 2 button platformers.

Get an NES emulator and then try Contra, Kirby, Mario, and many others from back in the day :)