With the modern ballistic tip or hollow point bullets designed specifically for varmint hunting all the calibers you list are able to have ONE HOLE in NO HOLE out capability on coyotes ,if driven to the correct velocity, and the shot is taken at the right distance, (no 25 and 50 yd shots).
Fox are 1/3 to 1/4 the size of a normal size coyote and would require a.223 or .204 light load, or a step down to 22 Hornet , .22 Mag, 17 HMR.