Mykal-- Like most other rifles, you must be cognizent of shot placement with the .17 Remington. I have used this caliber (along with others) for coyotes for about 20 years. Early on I was using the Remington 25 gr. factory loads. These bullets didn't expand much; rather, they acted much like FMJ bullets and seemed to pass right through the coyotes. This resulted in dead coyotes, but man was there lots of tracking.
I set the .17 Remington aside and used my .243 and 22-250 for about 10 years. With the advent of some heavier custom made .172 caliber bullets, I started using the 30 gr. Starke Red Prairie Varmint bullet in my .17 Remington and had extremely good success with that heavier bullet.
Recently, April 2004, I purchased a Savage 12VLP in .204 Ruger. That rifle was my coyote gun last season and will probably be my go-to rifle for coyotes this season as well. I use the 35 gr. FB HP Berger bullet for coyote medicine. I still carry the .17 Remington in the vehicle and if I need a backup coyote rifle, I will definitely trot out the .17 Remington and have the utmost confidence that it will do the job on coyotes!!!
The .17 Remington with the heavier bullet has plenty of range and killing power on out to 300 yards. If you and your rifle are up to it, you can make kills beyond that mark as well. Bullets like the 30 gr. Kindler Gold and the 30.8 gr. Hammett have very high BCs and are every bit as flat and resistent to wind deflection as most of the .224 caliber rifles. The big plus in my book, is the ability to watch the bullet hit your intended target when you use the .17 Remington and now I get the same experience with the .204 Ruger.