I have personally seen coyotes take down deer healthy deer. I have personally seen coyotes pull newborn calves out of cows, kill the calf, and chew off enough of the backside of the cow that the cow has to be put down. I've watched them trying to get into the cow/calves during calving, even with hands around tending to the cows. Some years it's been so bad we've had to post up a couple guys with rifles to try to shoot them off before they can get into the herd. If you let them, they'd kill every calf, and barely touch any of them. Just kill them and let them lay.
Coyotes are so prevalent because they are so adaptable. They are everywhere. From NY to CA. If you shot every. single. one. you saw, you couldn't put a dent in their overall population. They also work together as a team. That makes them very formidable predators, able to punch above their weight due to teamwork.
Back in AZ, there have been verified cases where 'yotes have snatched a small dog out of the arms of the old lady who was trying to protect it while walking down the street. In town. It happens.
They are opportunists. They're also lazy, they'll take the path of least resistance, or easiest meal for the energy expended. So, if it's easier to take your poodle out of your yard then to chase down that jackrabbit, guess what? Your poodle goes missing. That's just the way it is.
About all you an hope for is that you make it hard enough to get to your animals, or the risk high enough, that they pass on your place and move on to easier pickings. Putting a high velocity varmint bullet through a 'yote's chest is about the most sure way to stop them. But even if you scare them off (shoot and miss), they may remember your place, and go on to the next one, because THAT guy watches too many Disney musicals, and doesn't want to do anything about it.
To the OP,
The scoped 243 is probably your best bet. Any caller, or calling device CAN work. It doesn't mean that it WILL work. Especially if the individual 'yotes have been called before (and missed), or if they've heard the same call before. Coyotes can recognize the different calls, and just like we can tell the differences in peoples speaking voices, 'yotes can recognize the same call if they've heard it before. Especially if a bullet followed soon after.
I probably wouldn't even try a "rabbit in distress" call. That is way over used. By pretty much everyone. Start with something else. I've had great success with woodpecker in distress (yes, that really is a thing), "pup in distress", or even a mouse squeak call. I like the Foxpro E-callers, particularly the ones that have the "Fox Bang" feature. Which is, it plays your "normal" call, then when it's internal mic pics up the sound of a rifle shot, it switches the player to play "pup in distress". I've seen 'yotes that are sprinting full speed for the next county slam on the brakes and turn around when the player switches to "pup in distress" at the shot. The 'yotes are pre-wired (instinct) to respond to that.
You have to sit absolutely STILL. No f'-n moving around. At all. If you can't sit still for 30 minutes straight (about the longest you'll want to sit on one "stand"), then don't bother at all. All you'll end up doing is educating a bunch more 'yotes to ignore your (and other hunters) calls.
Unless it's a very young 'yote, and has been forced to hunt alone, it will have pack mates. Maybe 2, maybe more. Depends on your area. But when you start calling, at least one of these will try to circle in around and come in down wind of where the call is. This is how most "'yote hunters" get busted. They circle you, to try to figure you out. They either "wind" you (smell you), or worse (and less forgivable), they see you moving. Most of the time, when they bust you, you'll never even know they were coming in, as they will be long gone before you ever see them.
