RE: Lookin' for a good long range coyote rifle!
What do you consider "long range"? Personally, I consider long range to be 400 to 1000 meters.
From my days as a sniper in the military, I found that the lighter .22 cal bullets will drift a lot more than the heaver .30 bullets if you have any wind (depending on the wind value) making for a much more difficult shot.
Any center fire cartrige in .22 cal (.223, 22-250, .243, and 25-06 etc.) will kill coyots and other small game out to 500 meters and beyond (if you can hit them).
A good .30 cal (such as the .308 Win and .300 Win Mag) will make things a lot easier for you the shooter to hit beyond 500 yards.
You still need to master calling wind when shooting extended ranges no matter what you decide to shoot.
My personal choices would be the .223 for 400 yards and shorter and .308 for longer shots. The ammunitions is easy to find and there are a lot of different rifles chamberd for these popular rounds.