I assume you are not hunting coyotes for fur as even a 243 will ruin a coyote pelt. With that said, check out the ballistics on the 7mm-08.
I've got one in Rem 700 Mtn LSS and shoot 100 grn Sierra HP'sfor coyotes and 145 Speer HotCor's and 154 Grn Hornady RNfor deer, hogs & bear. Whileall shoot less than MOA,the 100 Grn Sierra HP's are especially accurate.
Don't know how many manufacturers make lefties in 7mm-08, but it's a great caliber that should be considered for your application.
firstshot
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Make your first shot count!