If I lived in a rimfire area, I would get a 22mag or maybe a 17WSM to shoot coyote.
Can you use shotguns? Shotguns with large shot or buckshot can be very effective. Early morning, late afternoon, anytime you can call are good times to call coyote.
If most callers are calling early and late, try the middle of the day. You might have great success because the coyotes aren't used to mid day callers.
My rimfire of choice has become the 17 HMR. I have a 22 Magnum, very accurate to 100 yds, great little groundhog bone crusher out to 75 yds, but out past 100 it isn't as dependable as the tack-drivng 17 HMR is
The 17 WSM would be a very good woodchuck taker in an accurate rifle. Unfortunately I bought a Savage B Mag that was just terrible. I tried all I could think of to straighten it out, but eventually returned it to Savage, who replaced the whole rifle with one that while better than the 4>5 moa the original managed, was only 1 1/2 moa on a good day. Hardly the 300 yd gun I hoped for when I purchased it. My Marlin 17 HMR was the rifle I got when the Savage was traded in. In fairness, there are some B Mags that are decent shooters. I know of one fellow who has one which he says does 3/4 moa any day of the week. I really dislike the idea of playing musical rimfires to find one.....My HMR is a 5/8 moa day in and day out.
As I said, I don't normally shoot coyote, but I did load up a box of 25 BB lead for my 12 GA that patterned well to about 50 yds, and did a number on fox and yotes hanging around the chicken pens at the other farm in SRA that I can hunt. Ballistics Products carries all the components you might need to load some up, including specs.
