Sleddog,
Big or small, to me any coyote is a trophy.
As far as "big dogs" taken with the Fireball, admittedly, I currently don't have one. I have had several in the past. Mostly XP's.
I really don't need to own one to argue the point that it's fully capable to take a coyote efficiently based on it's ballistics, if "shot placement" is proper.
I've taken coyotes and fox (as well as my hunting partner) with .222's & .223's for many years, as millions of other hunter's have. That's both in rifle and handgun configurations.
And the .223 in a 14" Contender barrel is a substantial bit less powerful than the Fireball is out of a rifle barrel, using the same bullet weights.
Regarding favorite coyote rounds used, I'd almost bet that the .22-250 is probably the top cartridge regarding coyotes, and the .223 a close second. And, yes, I'm sure the .243 is right up there as well as the .25-06 and others.
Not inferring that this is the issue in your case, or flaming anyone, but substituting cartridge power, for shot placement is the proverbial "fool's folly".
Sometimes hunter's have to pass up on those iffy, less than perfect shots, and I have. I think most will, and do.
A good portion of the time, if I can remain patient, a decent opportunity, more than likely, will present itself. I've taken all kinds of shots at various angles, like many have, and I've had the good majority drop on the spot. But, once in awhile, some, I've had to track a little ways. Usually, a very short distance.
But, that being said, it hasn't been the cartridge that made that decision at all as I've used many, including my .308. Even with restraint, it was shot placement not always being optimum, and I'll freely admit that.
Agreeing with you & all, things can't always be absolutely perfect, but choice of caliber rarely makes up the difference.
Based on what you were saying though, comically, if the .243 was the "Coyote gun of doom", then (if progression follows suit) the .308, .30-06, or .300 Win Mag should be, theoretically, the Coyote "Angel of Death", "Grim Reaper", or something. Kinda like Tim the Toolman...."more power"...lol.
Don't get me wrong, I honestly respect your opinion, and hunting experience, as you obviously produce results, and that's ultimately what counts......
Mainly, it's a "what works for you" kind of thing......but, that's not everybody, and the majority of hunters I know, and speak to in forums like this one, would greatly disagree with you on this point.
I don't know if you're hunting for pelts or what (as I don't believe it was mentioned) but the .243 (as with other larger calibers) more than likely, wouldn't be too pelt friendly, would it ?
As a daily passtime (that's turned into a business somewhat) I do a lot of load development for various calibers, and the Super Jet chambering that I've mentioned, was built (and based) after a large "in depth" survey of various calibers in the small .22 centerfire arena.
A rimmed cartridge was more or less preferred for the single shot action of the Encore, so it was a good choice. My efforts beared fruit, as this short barrel gun is a very sweet shooter and short wood's gun.
It's ballistics are twin, or on par with the .221 Fireball, and, like I mentioned before, very much the .222, but only falling slightly short of the .223, on half the powder charge.
Bullet velocity is bullet velocity no matter what cartridge it's shot from....that's a given.
Substituting bullet design in a smaller caliber, for the choice of a larger caliber entirely, can make it almost appear an equal based on visual reactions alone.
An example to what I'm saying is, knowing full well that the .243 is more powerful (for the most part) than the .22-250, using the right type of bullet for the task at hand can produce visual results that are "as devastating", or "more so", than the more powerful caliber.
The reason for that result is the animal's reaction to the destruction that that specific bullet style created. Almost like a small grenade going off in their chest
An explosive bullet, like the VMax, in the .22-250, in comparison to a regular softpoint in the .243, will produce far more devastating DRT's than the other.
Using the same style bullet in the .243 will make it even more so.
So choice of bullet, along with the velocity necessary to allow it to perform properly, can be used in any "reasonable caliber" to take coyotes.
Sorry for the novel.....again.
Take care & good hunting,
Bob