I would seriously look at the 223 for large coyotes, by the time you build one of the Cats and buy custom dies you could invest in a suppressor for the noise. Second would be the 20 Practical with a faster twist for bullets on the heavy end BUT you can accomplish the same thing with an off the shelf 204 Ruger.

After the first shot the rest are just noise.

Make mine a Minaska

Heaven has walls and rules, H-ll has open borders