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A .357 Benjamin Bulldog is definitely capable as is a big bore Airforce Texan. A stock Bulldog’s probably your best bet for that price range. I’ve read that AEA makes capable guns, but I’ve never used them and don’t know much about the accuracy and particulars of various models. They do seem to be affordable and powerful though. Maybe someone with experience with them can chime in.
No votes for the AAA Evol .30 for coyotes? (The Evol is directed toward @KevinTN’s post).