For those curious why I don't "want" to buy into another cartridge: Plain and simple, it's money. The less common cartridges cost more for both the rifle and for the ammunition. After a little looking it seems that I'll be out approximately $1000US for a rifle and a cache of ammo in .22 Hornet. Of course, if I begin reloading then ammo costs will be moot. Also, I just prefer cartridges that are very common in my area. Lastly, I prefer auto loaders. My .22 WMR is a Remington 597 and the .223 Rem is an AR-15. I haven't yet found a .22 Hornet in an autoloader and, if they exist, I suspect they're pricey.
The above stated, I do understand that my best option may be a .22 Hornet or similar. I'm just hoping I can safely use what I already have.
RE: Elevated Position... I guess I could buy a small elevated hunting blind but my guess is the coyote(s) would be gone by the time I climb up there.
After comments about .223 Rem, .22 WMR and shotguns... I've narrowed my options to .22 WMR w/ BT ammo, .410 bore shotgun w/ BB shot or .22 Hornet w/ BT ammo.
ETA: What do you folks think about .17 Rem with 17gr BT ammo?