you should look at the 243 its almost as good as the 6mm,you can shoot the hornady 58grain V-max at around 3760 fps and kill coyotes at those distances.If you dont reload there is a bunch of different factory loads from 55 grains to 100 grains.The 25-06 would be another good choice this is another good long range caliber.I myself would stay away from 22 calibers for this kind of range due to the simple fact that you will need a heavier bullet to maintain energy at 500+yards.I dont mean to insult any ones 204's or the well respected 220 swift but bullet weight needs to be 55 grains or more for this range on a possible 40lb or more animal.Many people have killed them at this distance with the 20's and 22's,but they won't be as capable of a killer as the 6mm/243 or larger would be,I read earlier that you were thinking about using the 7mm mag,I'm sure that you can kill them as far as you can hit them with that,they might have a little fur damage,on what fur thats left.For the most bullet selection the 243 has more than the 25-06 or 6mm combined if you dont reload.This is only my opinion,others may disagree.PS the 58 V-max shoots very good in both of my guns,savage110,remington 700,very accurate.good luck!