Small is right. First correct the reason for the thin grass. Moss is an indication of insufficient sunlight. Poa supina is a good bet.
Otherwise, you should go with a shade-tolerant ground cover. Such as: myrtle, pachysandra, ivy, Lamium, euonymous, goutweed, ferns, hosta and more. A statue, bird bath or fountain would help to distract the eye from the lack of grass.