Try contacting your local Wildlife department and see if they can help. Other than that you might try to bait the cat then shoot it when it comes too eat. I don't know if this works with cats or if it is legal in your area but it has been known to work in our area on problem coyotes.
Best of Luck!!
Ditto on checking with the wildlife department. They should have good advice on how to accomplish the feat. More importantly, if you do it the wrong way you could find yourself seriously afoul of the law.
Rather than spend my hard earned pennies on those cool Shoot-N-See targets or even the preprinted targets at sporting goods stores, I save a few bucks for weekend plinking sessions by using paper plates as targets. A 100 count pack of paper plates costs less than a 10 count pack of preprinted targets.
If you are playing with something like a semi auto AK, or building a young shooters confidence with a 22 or shotgun, those big eight inch blanks are perfect for putting holes in all...