Some retro suggestions:
- Super Mario Galaxy 1/2 - it sounds like your cousin is probably too old for this but this has one of the best "younger sibling" modes. They help collect and shoot bits. Which ultimately doesn't matter much
- The Legend of Zelda 4 Swords Adventure - It's basically multi-player Link to the Past! Bonus points if you dig up a GameCube, link cables, and GBAs
- Kirby Super Star - a mix of competitive and coop games
- Super Mario World (any) - you take turns but if you don't go 6 levels without dying to his one it can be fun
- Halo 1-3 + ODST - Great classic shooters, the campaigns are customizable for difficulty, and a little kid probably loves alien shooters
- Borderlands 1/2 - Looter shooters with a sense of irreverance
- Dead Rising 2/Off the Record and 3 - Zombie hoard murdering with combo weapons
- The Simpsons '91, Battletoads, TMNT, Streets of Rage, etc - Beat Em Ups are great for multi-player
Let me gradually increase the resistance on it each day until I can go Super Saiyan