One thing that wasn't mentioned was the proximity to cattle or other livestock. Bush or back country coyotes are few and far between. Getting close enough to them to use a 22 or 17 rimfire can be extremely difficult.
Another thing to consider, you may fool a coyote once with a call, but unless you have several different ones and tones, they will only work once on the same animal. If it spots you first, you might as well be telling him exactly where you are every time you use the call.
An interesting and annoying fact is that when a wounded prey call is used, every crow, raven and magpie for half a mile around will be circling your position within less than a minute. If they make you or are frightened by you, your position is busted.
A well scouted area with a good blind can be extremely effective.
Explosive bullets are a must, especially when there is a chance of a ricochet or there are other things or creatures around that may be harmed.
Accuracy is also a prime reqiirement, a No 5 Lee Enfield is just to powerful and doesn't shoot light explosive bullets well enough out to the ranges that are required. Remember, a coyotes profile is 2/3 hair. Very few coyotes measure more than 5-6 inches from spine to sternum. Maybe a little larger with a shoulder area shot.
Look for a rifle that will do the job that is required of it and will handle light explosive bullets. It should also have a decent scope that is capable of good first light visibility. Most coyotes are shot just before or just after sunrise, maybe a few in the afternoon or just before or after sunset.
A good pair of binoculars is also a must, again capable of low light clarity and definition.
Camoflauge that matches the terrain is also required.
I set up a dead pigeon on a stump on the edge of a field and pulled it back and forth with a string, maybe 2 or 3 inches at most, a coyote that I was watching, picked up the movement at 250+ yards, then looked straight at me, in snow/branch camoflauge behind a blind. I thought I was next to invisible, RIGHT, they live out there all the time and because their lives depend on it are acutely aware of everything around them.
Coyotes are also very territorial, and creatures of habit. Being extremely careful and completely aware of everything in their territory is a major habit. There ar only two things that will cause them to drop their vigilence, hunger and ### (dureing mateing season).
I would strongly suggest a sporterised, milsurp Swedish 6.5x55 with the lightest bullets that you can buy, if you handload, 95 grn hornady A max work great. These rifles can be had for less than $200 and a decent used scope for about the same price. This proven package will suffice right out to 400+ yards, if you do your part and learn how to shoot the distances and wind. This combo will work as well as any of the 22, 243, 25 or any other varmint rigs out there. bearhunter