you will need to be creative and perhaps use silhouettes of the sport appliqued on asian inspired fabrics. you get to really design your own quilt here. and while your son is adamant that mma is not karate, this style of fighting uses several martial art forms not just jiu jitsu. i have taken a coupla of jiu jitsu classes and it is more grappling than fighting.
mma contains boxing, karate, kickboxing, kung fu and a host of other martial arts techniques hence the name mixed martial arts. so technically you could use some karate fabric or images and not be wrong. you can include appliques of boxing gloves, the gi (martial art uniform), martial art stances, etc. there is a host of things you can do to design this quilt for your son. perhaps he can provide some input on what he would like to see so it will be something he will enjoy immensely.
good luck and i look forward to seeing your pics.
p.s. here is a martial arts quilt made with postage stamp squares
http://paulaobrien.wordpress.com/category/travel/tokyo/
