I have a H&R Hornet that I intend to hunt coyote with eventually, however, that is to 150 yards with comfort and expectation of a clean kill.
No one seems to have mentioned the 221 Rem Fireball. The starting brass may be pricey but it is a solid 200 yard coyote rifle, and is possibly the first upgrade/rechamber of the Hornet I will make. If it in fact will be an inter generational rifle, you will save 23% in powder costs over a 223.
If you use medium power loads which will hit hard enough to do the job at 200 yards using for example 16.8gr IMR3031 and 55gr bullets, you will get 400+ reloads from a pound of powder, and you should get excellent case life, helping to offset the initial case cost compared to 223. Saving 23% on powder over a year may not seem much, but over 60 years, if you use 1 pound of powder a year, you would save $6.66 in todays money on powder like L'il Gun, over 60 years that is $400, to some not much, to others the price of new Ultra Handi or a Marlin 30/30. Inflation adjust it and it will likely exceed $1000 or more by that time.
But if you want that occassional 300+ yd shot, for pure economy of factory ammo and cheap new or once fired brass, go for the 223, it will be around long after we have all graduated to that great shooting range in the sky, I am sure you can't go wrong.