In Iowa, coyotes are fair targets 24/7/365. There used to be a bounty paid for each pair of ears. But you do have the normal ordinances about shooting within city limits to deal with. That is mostly a matter to be discussed with your local P. D. in the case of nuisance or dangerous wildlife. Most cops are quite capable of being reasonable. I know one that used to shoot coons raiding trash cans just so he wouldn't get disturbance calls every week. Just remember: It is very difficult to pinpoint the source of ONE shot. Like Kenny said, firecrackers are easily mistaken...
Don't listen to any bleeding heart crap about coyotes, either. They are survivors and cannot be killed off completely. They are actually thriving and growing in number even as more rural areas disappear under the developer's dozers.
My buddy and I used to whack 'n stack 'em like cordwood for one farmer who let us bowhunt deer and turkey on his place. It was completely over run with coyotes. They would raid his chickens and geese in broad daylight with him right in the barnyard! Even the calves were killed regularly. He
hated them, and getting the DNR involved might only brings miles of red tape at worst, or a helpless shrug at best.
You have the right to shoot wildlife that threaten your property or family here, though one local farmer recently found the liberals around here can twist that right into a big fine and jail time...

Best thing to do is kill the varmint quietly and keep your mouth shut about it.
That farmer offered us a free tank of gas in our pickup for every coyote we killed. We happily did it for the sake of the almost extinct pheasant population and the declining turkeys. And for FUN!! No thanks or gas needed!
Staking a live chicken out isn't exactly kosher, but it sure works and chances are the coyotes would get it anyway if left in the barnyard. (squawk!!) Just make sure you hide REAL good! A coyote makes deer and turkeys look blind and deaf! They are smart! A 12 gauge semi-auto or pump loaded with 00 Buck makes a nice close range impression, especially when there is a pack of them. For longer range rock 'n roll, it is tough to beat an AR-15 on coyotes, imo.
Arrowing a coyote is REALLY tough! I have only killed 3 in all my years of bowhunting. I have been busted just trying to draw my bow while concealed in a treestand more times than I can recall. Their eyes are positioned both in front, to the sides, and on top of their heads and they see EVERYTHING all at once: in front, peripheral, and above. You really need a blind for coyotes, and they are too smart to go very near one. Blink your eye, much less move to draw, and they instantly detect the motion.
I was walking back to camp one day and crossing a fallow field of weeds when I saw a plume of dirt go hurtling skyward a little ways off. Soon, another followed. And another and another... WTF? I
had to investigate this! With an arrow nocked, I crept up on the spot to discover a coyote with his head and shoulders down a hole he was enlarging in a fury. I walked right up to within touching distance. He was too preoccupied to notice. Coming to full draw, the delimma was "Where do I shoot him?". I finally settled on the puckered little brown star right beneath his tail. I put that broadhead and arrow all the way through him lengthwise! He went straight up into the air, came down on his feet, ran into my leg, and tore off out of sight in the blink of an eye. So fast, he never even left a blood trail! But there is NO way he survived that!
The other two I have killed with my bow have been coyotes that I heard coming and, thinking it might be a deer, came to full draw before they appeared. Even then, they are quick enough to duck an arrow at the sound of the release. Those dudes ducked the wrong way.
And hearing!! Holy cow! I was watching a TV special on Yellowstone wildlife during their harsh winters. They showed a coyote walking along the deep, crusted snow and hunting mice WAY down beneath it by
listening for them!!
If shooting those coyotes before they kill your dog is not an option, snares can be very effective. Especially if you can find a hole in or under a fence where they cross with regularity. Snares kill, so be sure only coyotes are likely to be crossing there! But they do kill quietly!
I also think a simple . 22 with a sub-sonic load will do the trick and not get any attention from neighbors. Don't ask me where to get sub-sonics, I've never shot one, but they are out there.
Sheesh! If me and my neighbors called 911 every time we heard gunshots next door, we'd need to keep fresh coffee and donuts on hand all the time! Woodchucks are a big problem on my property as well as my neighbors'. They are terribly destructive and undermine buildings. It's REAL hard to put dirt back under a concrete floor! I keep loaded . 22's in all my buildings just to be sure one is real handy when I spot one. Live traps are a joke, and there are too many neighborhood cats and dogs to use leg or body traps or snares.
We have coyotes all over out here, too, but they haven't killed any neighborhood dogs that I know of. Probably a few cats, but there's an ample supply of those. It takes a pack of coyotes to kill a retriever-sized dog. Lapdogs, well... :{ My old Golden ripped the crap out of coyote one day out pheasant hunting. He hated coyotes, fox, and possums. Skunks, too, but several trips to the carwash in the back of my pickup when he was a pup taught him to growl but stay clear of those! :-laf He was a very big (NOT fat) Golden, and he needed a few stitches after, but the coyote definitely got the worst of it. I couldn't shoot for fear of hitting my dog with the 4 shot I was loaded with.
You might actually try lighting a firecracker or two (or a hundred) the next time you hear or see coyotes nearby. One guy at work swears that works.