the OP also didn;t mention if he is trying to save pelts
if so, I don;t think the .357 is a good choice at all here, as it will damage the most fur, as will any LARGER caliber center fire caliber will, that some mentioned as in .234-.270 and so on!
yes they will kill them but at a cost to the fur!
most any center-fire .22 caliber would be a better choice for coyote work from a 100+ yrds , with limits set on what caliber .22 is used!
.222, .22-250, .223 .224 all fine coyote calibers for longer ranges with advantages based again on caliber and bullet being used in each!