It's not all that rare to get two opportunities on coyotes. They may not come in together, but I shoot several doubles a year that would be more challenging with the distraction of reloading a single shot. I have a .22 Creedmoor that I coyote hunt with and it's a stellar performer. Not exactly the most fur friendly of cartridges, but it's clearly a more capable killer than the .22-250's that I've shot coyotes with for the last 50 years. One thing that should be brought to your attention is the feeding issues that can be present out of the standard Remington magazine box. The taper in those boxes make it a bit crowded for the .22 Creedmoor case, and in spite of some glowing reports of how well they feed, you will likely have suboptimal (and sometimes just plane lousy) feeding performance. If you choose to build one, I would strongly suggest going with a AICS style magazine with the appropriate bottom metal for that mag.
My rifle is suppressed, and I get a big $hit eating grin when I hear that bullet hit tissue way out there and see the coyote fold up in the scope. IMO, a set of case forming dies to neck down the 6.5 Creedmoor to .22, was the best thing to ever happen to that case. If your build one, and it's done right, I guarantee you will like it.