Light recoil rifle for coyotes and antelope?

My hart barreled rem 700 243 would do it easily. i shoot it in 500 and 600 yard f-class matches. but not with factory ammo. a factory rifle with factory ammo at 500 yards . maybe a 40x or sendero or lrp . a sako 85 .243 varmint , maybe. maybe a 25-06 sendero.
 
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