Do you plan on selling the pelts from any coyote you shoot, or are you just looking for a little pest control? The .243 Win would suit you well, but I'd lean toward the 25-06 personally. It'll do more damage to a coyote pelt, but there are loads available with tough bullets that will minimize this with the .25-06. It'll knock 'em dead WAYYYY out there too, if long shots are your thing.

Mike