The ultimate predator rifle, depending on where you live, is often a shotgun.
Don't buy into the fantasy that it's like what they show on TV. Big coyotes running in across wide open country just begging to get shot at.
The reality for a lot of us east of the Mississippi is ultra-wary dogs in thick brush country and often the shot comes at bayonet range, not rifle range. When I call in a coyote, it's more likely that I'm going to have to push him off my lap than it is that I'll have a standing shot at 200+ across an open field.
I have stands where I carry a rifle, but the shotgun gets the call 80% of the time.
Don't buy the hype, buy the reality of your situation. Using a rifle at shotgun ranges is a disadvantage, not an advantage, believe me. Bottom line is don't buy the tool for somebody else's job, buy it for yours.
Grouse