A ground cover worth trying is Perennial Peanut. There are two species on the market. Arachis pintoi and Arachis glabrata. The former is a faster growing species with fleshier more tender leaves and rhizomes. This species will cover a large area in a relatively short period of time, but it is more tender and will not tolerate foot traffic. The latter species is slower growing, with smaller firmer leaves and rhizomes, which will tolerate foot traffic. They both produce yellow pea shaped flowers that are edible and have a faint taste of peanuts, thus the name perennial peanut.
Richard Lyons nursery has both species in stock.