Be a parent. Say no. An 11 year old will change his mind often. I don't care if you're punk, that's just being reckless, careless, and unfit!!
What artist in their right mind would say yes to tattooing an 11 year old!!
Besides, his body isn't matured yet. He's still growing and if he were tattooed now and hit a growth spurt, the tattoo will be distorted.
Think carefully: If you were allowed your every whim to be indulged as a 11 year old, how would you turn out? Probably a mess, no doubt.
I suggest giving him a packet of fake tattoos and have fun. Or letting him draw on himself with colored permanent markers. Who knows, he'll get out of this phase and turn goth. Then turn around to be a preppy boy, haha.
Punk rocker with her head on straight