I have to assume you 1) have fired a rifle before and 2) know how to properly use it. If either of those is wrong, stop before you do anything. Get some training before you do and go fire some different rifles first. Also, I have to assume you live in a rural area where firing off a round or two won’t be a problem. Again, if not, better stop. In a city, you’ll get arrested so don’t even try it.
Coyotes are tough because they are extremely skittish around people and like to hunt when they have the advantage, like at night. If they see you, they probably won’t sit still long enough to get a shot off so concealment is key. If you can get a wounded animal call that will help draw them in, but they can usually see you before you see them.
As for the rifle, anything above a .22 LR would do the trick and even a well placed shot with a .22 LR will kill one. Just a little harder. If you have a wide open space, I’d get something that shoots fast and flat. A .243 or .22-250.
Some guys use a .177 air rifle, which isn’t like one you buy your kids. It’ll take them down and is quieter, but I would rather not take a chance. If I were to go with something with a bullet that small, it’d be a .17 HMR, Hornet or WSM.
A .204 Ruger is a good caliber, too, as is the .220 Swift.
Bottom line is get something you’re comfortable shooting, practice and get good cover.
Good luck!