I'm not a huge coyote slayer to begin with. But my county here in NC is restricted to rimfire & shotgun. Deer hunters have a muzzle loader season, but they have to be so many feet above the ground. I think it's 15 feet. At any rate, I've killed 6 or 7 coyotes here and all have been with the 22 mag. I bought one of them 3000 + fps RF jobbers in order to retire my 22 mag from such duties and have not shot one since But in other areas not RF restricted I have my CZ 527 Varmint in .204 PS.... I don't think your going to match that blondie. You might consider making Glen a pair of slippers out of her and start from scratch on that throw.
I'm from Ontario, Canada, and we don't have caliber restrictions for coyotes. We do for pretty much everything else. I think if I was to go center fire I'd go 223 only because as far as I can tell, ammo is cheap. However, others here will know more than me.
I wish I knew how rare that dang blonde coyote was, I'd have skinned out the feet to make a wall hanger. What I'm going to do for the throw is collect, flesh, and tan every coyote I get until I can start fur matching (see you in a couple years ).
Ammo cost for shooting coyotes isn't really a concern. At least it isn't for me and the number of coyotes I shoot. Nothing wrong with a 223 but I wouldn't let ammo cost dictate.