i dont really care for savage cause they seem to kick harder then the rest. you might want to look in to a 25-06 i bought one for the fun of it and really liked it i took 6 deer with it but the only thing is it doesnt leave that much of a blood trail

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30-06 will make as big of a mess as a .303. Most of the 20 cals make nice coyote rifles. ,204 ruger,220swift,221fireball,222rem,223rem,22-250,.243(not fur friendly) I think your best bet is a .223 loaded with some sort of V-max bullet. My best results are with the Black Hills 60 grain V-maxes, and the Hornady 40 grain v-maxes Mind you a v-max bullet is fur friendly but will be a whole lot better than a 303