Colleen, I too and so very sorry you cat was taken away by coyotes. That is a threat here where I live too. Coyotes and bobcats. I am allergic to cats but have dogs. My best little hunter, my Jack Russell, passed away 2 1/2 years ago. I miss her terrible. She was a terror to mice and squirrels.
You might look on Amazon at a product called the Rattinator. It's a trap. I don't have one, but I am considering getting one. A friend in South Florida has one and swears by it.