Actually, "coyote gun" can mean any of many different things.
What many consider a "coyote gun" is heavy, with a long barrel, and it'll usually shoot tiny groups.
But for me it means a calling rifle. When calling coyotes, shots are, more often than not, close in and fast. A short barreled, small caliber rifle that's light and handy works great. Accuracy is good if the rifle has it, but it's not required for this type of hunting. A long shot on a called coyote is 300 yards, and that's about as far as I care to shoot at one with a .17 Rem or .223. If the rifle will shoot inch and a half groups at 100 yards, I'd not frown on it. I can shoot tiny little bug-hole groups with my .17 Rem, but it doesn't make a lick of difference when shooting at a moving coyote at close range.
My advice is to decide ahead of time how you intend to hunt with the rifle, and build it according to your needs. It's all a matter of perspective.