NY Boy,
I am late to this post, and it looks like you have already arrived at the best conclusion - without question. Congrats on your good sense!!
That said, I feel the need to chime in only b/c I was a bit taken aback at some of the recommendations that you got, and I feel obligated to to provide some additional color for you to consider.
First off - I need to say that while I am fairly new to chickens - I am not new to firearms. I am a Certified NRA Rifle instructor, and I have shot competitively on and off for years. In addition, I used to be a pistol instructor, have worked as a Range Officer on two different ranges in my community - and have been handling firearms of all varieties since I was a kid (I am now in my late forties... I don't want to do the math.)
First Observation: New York has some of the toughest Firearms laws in the nation. Before you do anything, check with your local sheriffs department to see what your State, County, and City ordinances are. Also - if you live within X yards of a school, a hospital, or a state/federal facility, there may be different restrictions to your residence - specifically. (Varies by municipality and state.)
Next Item: If the firearm was for home defense rather than animal predator, I would generally agree with the folks who recommended a shotgun. HOWEVER, a shotgun (unless you are shooting slugs) is going to blow a REALLY BIG hole (of ever increasing size, as distance increases) in anything in the downrange vicinity of your target. If your dog, your cat, your chickens - OR YOUR KID - is in the teeth of the varmint, you're gonna shoot the victim as well as the perpetrator. Not a good solution. It's only a good solution if the target is standing in your doorway pointing a gun at you. It's a last resort defense against the worst of the worst bad guys - or the tool of a lazy hunter who never learned to aim. That's my opinion. Others will disagree.
Next Item: Some well-meaning folks recommended a revolver. I have handled just about every make of hand gun there is. I am a reasonably skilled shooter - even under pressure - even with the adrenaline pumping. To put it bluntly, I can't hit the broad side of a barn with a revolver. It's the tool of "Cowboy Action" shooters, or people who have never fired a well-made semi-auto. They are safer - if only b/c the trigger pull is (from the factory on most models) about 6 lbs which is enough to cause an inexperienced shooter to "pull" well off target. (Meaning you are gonna hit something other than the coyote, and if you miss wide - you may hit the six year old kid three block away playing in his yard.)
Back in the day, people had no other choice but a revolver. Just like people had no other choice than a straight shift car. Today - you would not teach your kid how to drive his first automobile using a straight shift. And a first gun for any new shooter is NOT a revolver.
Next Item: Unless you are willing to shoot to kill and do it without a second's hesitation, you have no business with a gun in your hand - or in your home. And - if you have a gun in your home - EVERY member of your family needs to be familiar with its operation, what it feels like when shot (not just dry trigger pull), as well as what it looks like when a living creature is shot with one. Specifically - you need to see what a poorly placed shot will do to an animal - and you need to practice, practice, practice - until the tool is an extension of yourself to such a degree that poorly placed shot is a very remote possibility.
My recommendation... if you have Coyotes; baited traps and relocation. The wildlife department can help you with that - especially if you can demonstrate that they have taken pets or livestock.
One thing that I have found helps too (particularly if you are a carnivore - doesn't work as well with vegetarians) is urinate on the perimeter points of the property. Coyotes (and other predators) are territorial creatures and they are (generally) afraid of humans and other carnivores. If you "mark" your turf the animal will understand it. If you see him - become aggressive and growl and bark, kick the dirt, and run toward him flailing. He'll get the point. You'll be speaking his language, and you are bigger - he'll take the warning.
The air horn will help too.
Hope this helps a bit.
--Grace.
