I don't see why they wouldn't I can get armor piercing ammo for an AR, what's the difference? I can look at an FN catalog they have about 5 ammo variants none specifically say armor piercing( which I don't think the catalog is hiding anything it has the m-249 to the FN M3M .50 cal MG in it) but that is because the round has armor piercing abilities in its design, its just the nature of the round it's nothing extra.
its about how hot its loaded and how fast its moving more than cinstruction. spoon point, FMJ and AP rounds are banned from civilian ownership. frangible, HP and BT are OK or you can load your own if you;re a glutton for punishment. the civi rounds are downloaded over 1000 FPS slower than the military full power rounds.
there have been small quantities of spoon point full power rounds found at gunshows but no one knows where they come from. its generall several boxes at best. ive seen one full case of LEO surplus sell off full power FMJ at a gunshow that sold for over 1000$.