I agree with a .22. Buy a semi auto so you can put 2 or 3 rounds into the coyotes. It doesn't get any cheaper. Use CCI minimag hollow points for ammo.

GM1

I'll cast another vote for the .22 LR.
Get a decent rifle, though, so that you can put rounds exactly where they need to be. At less than 30-40-50 yards, if you're good and solid, you might be able to get the head shots with a handgun.
I wouldn't take heart and lung shots on a coyote with a .22 at more than 30 yds or so.

CCI Velociters and Rem Yellow Jackets might be other options for you, too, if you can't get your hands on CCI Mini Mag.
Velociters out of a revolver with a 7.5" bbl have been used as a cat, yote and finishing gun in AZ and MT, and a general pest gun.

Help yourself out with aiming and grab some solar motion-sensor garage lights or at least some solar stakes that will last through your night, and pre-mark your distances if you end up shooting something or at ranges that need adjustments. That way you can have the best conditions for a clean kill.

If you get a bolt or pump instead of a semi-auto, you can also shoot subsonics, which keeps practice noise down and at 30 yds a few of the subsonics are fine for foxes and other pests, and for small game taking advantage of your feed.
There's no recoil to fight with a .22 and you can usually use your thumb and first finger to work the bolt and a middle or ring finger to make your shot, barely coming off the trigger at all (or not at all for a pump).
It can be done with an 8mmM, although that big boy is practiced for plate-sized targets, not soda cans. You can hit your soda can and playing card doing it with a .22.

I would not get a single shot for a predator or game gun, period. I'd save up for a slightly less accurate bolt, pump or semi before I went with a single shot, for the very reason GM1 said.
-P

I will make the assumption that hunting them is legal in your location. If this is the case then why do you need neighbours permission to do so?

Some of the fields around us are owned by neighbours, and it is more of a courtesy than anything, especially as one of them operates a kennel next door with plenty of customers coming and going. The coyotes tend to approach our farm through the neighbour's field as well, so having permission to shoot them before they get to us is nice.

Saw the PM of 50-60 and probably under 100 yards.
Drop my suggestion about subsonics and handguns.

At the outer reaches of your target area, you might have the lack of penetration you were worried about.

A couple of people makes an inexpensive .223 bolt. That loses some of your "quiet" and inexpensive ammo options, but they're good predator guns and you can use them to take non-elk, non-muley deer pretty easily, with good shot placement and distance awareness.

Savage's Axis/Edge springs to mind. It used to be about what a 10/22 costs in the U.S. The Stevens 200 is plenty accurate enough for what you're talking about. Both are at or under $300-350 USD. A little more would get you the Savage 110. If you get the Axis, you can stick an optic or scope on it, but it really doesn't have any aftermarket parts for people.

You would need to check local and regional availability, but the .22-250 is PHENOMENAL. I love my grandpa's. I wouldn't go after bear, Louisiana hogs, or muleys with it, but it's got plenty of power for wolf, bobcat, antelope, javelinas, small to average whitetails even with heart shots, and coyote, and it works well with head shots on groundhogs, rabbits and prairie dogs and neck shots on gobblers. You may be able to find decent used ones inexpensively, but ammo selection and availability may be more limited than a .22 or .223. That should play a factor.
It also has a big crack-snap sound, way more than a .22, but it's not a big boom like traditional deer calibers.

Inside 100 yds, especially staying inside 50-80, a 20- or 12-ga slug or a little closer buckshot is also a viable option, although you're looking at a BIG boom at that point. Inexpensive shotguns abound, and have been discussed in at least a couple of places on this site with the pros and cons of various models and types.

If you want to stay quieter but have a little more power than a .22 LR for distance knock-down, you could look into .22 WMR/.22 Mag. That, too, may come down to the regular ammo availability and selection near you.

Or, stick with the .22LR and wait for it to be inside the 40-50-60 instead of taking it at 80-100.
That's where I'd really lean. Plus, at 40-50, you're at a range where you can reacquire and put on extra shots as needed without the yote already being at the verge of your killing power and personal range when it stops and runs the other direction if you jerk or sneeze or slip or something.

I think a .22 is too small for humane kills beyond 60 yards. Oh sure, they'll die but they won't drop on the spot. Maybe a magnum would do if your shots are all close- under 100 yards.
Aside from that a .223 is good for varmints only. I would be thinking deer caliber .243 or .270.

Do you know anyone who reloads at all? If you already have a larger caliber rifle and can get someone to work you up some subsonic loads this is ideal. They'll be quieter than a .22 WMR and pack a punch.
Pistol caliber carbines would work just the same.

.22 will kill a Coyote under the right circumstances as in short range, little wind, precise shot placement etc. You will find trappers out there who has killed "thousands" of Coyotes with a .22 but reality is that most Coyote hunters steer away from hunting Coyotes with a .22. So its possible but not recommended. Not to forget that most Coyote hunting is done at distances which the .22 are not particularly effective at. You need a bigger caliber such as a .223. or a.270 which are also two very common calibers and ammunition should be available in abundance now and in a shtf situation :).
I recently started going out with a mentor to learn Coyote hunting and he uses a bolt action .223. For this type of hunting I purchased a Savage Axis .270 package. It cost me $ 360 in Fishing World in Hamilton. First impressions was that the gun looks cheap. Cheap plastic frame and magazine was not good first impressions however the scope was a Bushnell and the barrel, receiver and bolt looked decent and then of course the price. However I remembered sighting in a friends up north and the .270 was a joy to shoot so I decided to give it a go as I was eager to add that caliber to my collection.
Took it to the range to sight it in. Boy does that thing shoot straight !. It was a joy to shoot and very accurate too. The rounds are super fast and I am now looking at reloading some 3200+ FPS rounds as I was told that fast is better when hunting Coyotes. But it is loud... The only way to mitigate that would be to drop down to the .223 caliber. But even with a .223 caliber gun you will drop the Coyote with one shot at decent ranges. But the Savage Axis line of rifles are great value for money with a decent scope included all for a low entry point in terms of cost.

Didn't think about it before a crossbow would also work and be completely silent. Most shots will be at known ranges (25 to the tree, 30 to the fencepost) and the hardest part of bow hunting is knowing the exact distance. Maybe no more than 30 yards to start, 40 as you get better.
For all the advantages a crossbow should be a required prepper tool anyway.

If you want a rifle for small game and yote, I prefer something in .22 caliber.

If you want a rifle for small game and yote, I prefer something in .22 caliber.

I am curious as I am learning to hunt Coyotes at the moment.

What is your practical experiences hunting with an .22 ?. A lot of preppers talk about "hunting small game" with a .22 so it sounds easy and very common. I did not think that a Coyote was considered "small game" and I have just never meet anyone hunting a Coyote with a .22 so I am interested to learn what your real experience and practical advices are ?.

I suppose he could have meant a centerfire .22. They're the classic varmint rifles. Small centerfire case, very fast bullet, flat trajectory. .223, 22 Hornet ,22-250 and a few others
Not very quiet and all you'll be shooting are coyotes and groundhogs. I think .243 is the smallest you can legally use for deer.

Well I am eager to learn :).

A .22 cal can easily kill a coyote. They don't have the accuracy of larger rifles over 100 yards or the hitting power either. We could still shoot deer with one in my youth but they were later banned for large game due to too many animals being only wounded. A well placed shot has the ability to kill a man and the .22 cal has been a favorite for assassinations other than on TV. But if you have a larger rifle, you can more easily place a long distance shot with less effect due to bullet drift and trajectory and most times you see the coyotes at a distance. I would suggest using a .222 as this is also more humane to kill quickly.

I've killed coyotes out to 100 yards with the .22 LR. Generally they run about that same distance before expiring. I've also shot a cougar with the .22 LR and it went down faster than the ones I've shot with larger calibers.

The advantage to .22 caliber (either in rimfire or the various centrefire calibers) is the small hole they make in the pelt. Fur prices are apparently on the rise and you don't make anything off a prime pelt shot with a deer rifle.

Get the .22 LR if you just want to harass the 'yotes but a centrefire .22 for a serious predator rifle.

Just my opinion,

OG