I also was surprised at the number of 243 suggestions. I hunt S. Az and while I have killed a few coues with the 6mm Rem and one with a 243, I vote for the 7-08. It is more versatile and when she gets around to hunting elk you won't need a different rifle.
Start with reduced loads for practice and use full power loads for hunting. She will be able to handle it IF the stock fit is right plus a good recoil pad. Heck you can add something like the shooter's friend from Cabelas for bench shooting. It makes a huge difference. A 120 Nosler ballistic tip would be a perfect bullet for the 7-08. This bullet killed many coues from my slightly more powerful 284 win. I have read that the 120 nos bt is built tough and many on 24 hr campfire have raved about its performance. It always exited the coues I shot out to 450 yds.
link at shooter's friend:
Cabela's: Search Results