I think a .223 in an AR platform would be significantly different than a bolt action .22-250. Sure, it may shoot the same diameter bullet but, from a predator hunting perspective, it gives you a quick follow-up shot if you need one. Plus, if you're not too trigger-happy, it can be significantly cheaper to feed. If you're still not convinced on a .223, .204 is a good option. However, I feel like the effective range is still kinda limited for coyotes, unless you go with a heavier bullet. In that case, you're right back to a .223 anyway. Last, but not least, you could look into the 22 Nosler or the 224 Valkyrie. I haven't had a chance to read up on either yet, but both look like they have a lot of potential for coyote hunting.