I would not build an AR-10 for a coyote gun. The weight and size is just not needed. But if I were to build an AR-10, I'd look at the 22 Creedmoore. I have a 22-250ai and the Creed is basically the same or better without fire forming. Though a bolt gun would be a better choice.
I've killed a lot of coyotes with a 223 using 40, 50, 55 and 77 grain bullets, they are not hard to kill. If you're gonna snipe one instead of calling them in closer, I'd go with the 77 gr bullets for less wind drift. I shot 600 yards last week with a 55 grain NBT and had to hold a mil and a little more windage with what I considered a slight to moderate wind. The 77's kill just fine.
