We love our pets and our plants, but what do we do when the two don’t get along. Some inventive options for ground cover, that can withstand your pet, are: 
Asparagus Densiflorus Sprengeri grows about 10 inches to 20 inches tall, can be trimmer and can fill an entire portion of a yard if not trimmed back. Asparagus fern is an almost indestructible fern/ground cover that can take full sun, part sun, or shade. Be wary, as it can spread quickly and become the dominant plant.
Myoporum is a great little ground cover that flowers twice a year. This is a drought tolerant ground cover, that can you can trim with a lawnmower.
Society Garlic Tulbaghia Violace is a beach ball shaped low growing shrub. While not a ground cover, it is a natural deterrent for cats. A little Society Garlic and some bark or rocks to fill in the rest and your area will be cat free.