I have a friend who is a former Marine instructor. He taught his guys how to make 1000YD kills with an M16. The method used was to "walk" the shots in, not a "first shot" hit, but the (62gr?) ball ammo would do the job.
I have shot prairie dogs past 500YDs with a .223, but wouldn't shoot coyotes at that range using light frangible ammo (V-max, Ballistic Tip) without some info/testing of the terminal ballistics.
I enjoy long range shooting and in 37 yrs have shot many 10s of thousands of rounds past 400YDS, field and competition. My personal "rule of thumb" limitations for long range coyote (with heavy barrel accurized rifle and proper ammo/conditions) would be: .223 to 500YD, .308 to 900YDS, and then my 7mm mag to 12-1500YDS. Someday I'll have a .30-404 built and try to shoot them at a mile +.
The real secret to long range shooting is to push your limits on paper before you go into the field and practice, practice, practice.
Leon