Really any rifle will put a coyote down, they're easy to kill. When people are building what I'd consider a coyote gun I typically think they want something that wont damage the hide. A .30-06 is a fine coyote gun if you don't mind having to carry the two halves of the dog.
I'd stick with .223 for coyote because ammo is so stinkin' cheap compared to .220 SWIFT, .25-06, .22-250 or any of the other widely considered "Varmint Calibers". .223 is plenty accurate too when hand loaded.