RE: .17 HMR or .22 MAG
An outdoor range that only allowed rimfires? Think I'd be for finding another range?!
If you're calling them in, either is so-so in terms of reliably knocking down a coyote. At close range, a hit is a hit and will oftenkill, even with a good .22LR. However, even at that range, it'soften easy to overestimate the size of the target and send a bullet through nothing but fur - and it won't matter then what you're shooting. That effect is amplified as the range increases. I wouldn't say they're terribly tough, but I've had coyotes take a 50 gr V-Max from a .223 at 100 yards-plusand still require a second shot to finish them off. If I know I'm going to be shooting coyotes beyond100 yards, I generally take a .22-250 or .243.
Were it me, I think I'd make sure your sonhas a good, lifelongquality .22LR to take to that range, and find him adecent used .243.The 75gr V-Max (which is alsoloaded commercially) is death on coyotes, and he'll beable to hunt deer with it (in most states)as well.If he decides he needs something bigger one day, let HIM make that choice.