RE: .243win bullet for fox
Foxes aren't really big enough to justify using a .243 on. If you're looking to save the fur, I'll second looking toward a .22 Magnum or maybe a .22 Hornet.
I HAVE seen FMJ .22 Mag ammo, but I'm not a fan of FMJs on Coyotes with a .223, so I'll not recommend FMJs for foxes, either.