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.
A perk of majoring in wildlife biology in college is the plethora of hunting knowledge that you collect throughout your course load. One of the most important factors in whether an area can hold large quantities of animals or produce large antlers is forage.
Most universities, state schools and even community colleges offer basic botany courses and plant ID courses. Although it might not be feasable for the average middle age hunter to pay tuition and go back to college to learn hunting...