The boom-box cover gets VERY hot, so I think normal paint wouldn't last too long on it as it comes, and I think that's why Kawasaki didn't paint that piece on the green/white/black '09s even though the rest of the lower fairing is green (it looks dumb IMHO).
My proposed solution will be to get (or make) a link pipe with brackets to eliminate the boom-box but keep the cover. I believe the reduction in size and mass and the increase in distance from the hot parts will seriously reduce the heat put on that cover, allowing that sexy blue to hold up on there as well as anywhere.