I just wanted to let some of you know, that I also have a couple of Remington factory rifles that are very accurate downrange. I don't believe I will be shooting any coyotes through at a mile away! It sort of takes the fun out of being able to watch that critter before his demise.
Now getting back to those rifles, one is a Remington 40X in a .222 and shoots 1/4 groups all day long, come rain or shine at the bench. The other is a bull barreled rifle, known as the 6mm Remington. It shoots groups around the .350 at 100 yds using Sierra BT bullets.
However, we here in my state of Missouri, just don't get those 1/2 mile long shots like some may in other places out West etc. My model 70 sporter in the 25/06 caliber shoots .600 to .750 groups at 100 yds, depending on the weight of bullet I choose and once again using my handloads. Now the model 70 Winchester in the .243 caliber will also shoot .450 to .600 groups at 100 yds with my handloads of course. These rifles are plenty accurate enough to take any coyote size animal out to 500 yards.
The 6mm Remington, along with the pair of model 70 Winchesters in calibers .243 & 25/06, are capable of taking any coyote down range. The problem is generally with the person pulling the trigger on any of those rifles. It also helps to have the knowledge and shooting skills for those far out youndar shoots I hear about so often nowdays. The nailing of a coyotes hide to the barn door is a whole lot easier at 200 yards than at 600 or 800 yards.
I think for some, it would be better to place a 3 gallon bucket out at 600 or 700 yards and see if you can put those first two shots out of your rifle into the bullseye. Yes, that bucket is going to look awful small once you hunker down over the rifle scope to take that shoot. Practice, Practice and a heck of a lot more proper Practice is what it takes to get the job down on any animal that far down range. Good Luck! Good Hunting!!!