.243, 6mm, 25-06 are all good rounds for antelope. All will be a bit rough on coyotes if your after the fur, unless you handload them down. That being said, some use full metal jacketed, solid points in 30 calibers with minimal fur damage. Antelope go down easy.

If your a good longrange shooter, than the 25 06 might be better. I disagree on the necessity of many long shots on antelope. The longest I've taken was 250 yard. All of the rest of the goats we have shot have been within 150 yards, with most within 100 yards. They are huntable, and stalking in on a herd of animals with that kind of eyesight is a good challenge and a blast!