Someone correct me if I'm wrong, but I was under the impression that almost all predators are shot well within 300 yards by calling them. I doubt you'd see a coyote at 500 yards. If I were looking for a dedicated predator rifle, I'd probably choose a 16-20" barreled AR-15 with no more than a 10x variable power scope on it. The reason I'd choose such a gun is because it'd be highly accurate, portable and more than powerful enough to take a coyote at 300-400 yards, but not so powerful that it'll completely destroy a pelt if you plan to sell them. And it's semi-automatic and light recoiling, making for ultra-fast follow-up shots if you miss a moving coyote or have multiple dogs come in at once.

Mike