redhawksixsh, I have both and use a .22 Mag for coyotes out to about 100 yards, very effective with good shot placement. However since you rleoad I highly suggest the .357, you can tailor your loads and Kieth design semi wadcutters loaded to .38 Special velocities, or even store bought .38's or .357 Mags (if needed for long shots) or hollow points, if loaded fast enough to expand, will do perectly for coyotes and even more. I really like my .22 Mag but in this case it's a no-brainer, the .357 is the MUCH better choice....<><....
P.S. - I think .38's are quieter than .22 Mags and .22 Mags are about equal to .357 Mags for loudness if this helps, for sound I would go with the .357 Mag, especially if loaded to .38 Special velicity, and for effectiveness as well. Both the .38"s and .357's would have more "knock down power" in my opinion, especially at any distance....