I live in west-central Florida and would like to put a cover on my hot tub.  It does get cold here in the winter (25 is cold when you have coconut and royal palms)  I use my tub year round due to severe Restless legs syndrome.  The bubbling water overdrives that unpleasant sensation).  The issue I have is with my two cats.  They like to spend the days out on the pool deck. Unfortunately, despite having a Cat Genie litter box (washings itself and pumps the waste into the sanitary sewer) in a bench box with an access door on it, one of my cats will occasionally pee and poop on any large flat horizontal surface.  Obviously, I do not want to build something that will turn into a makeshift litter box.
I would appreciate any helpful suggestions that do not involve shooting, hanging or otherwise killing the cats.