It sounds like a really tough site, so I'm going to recommend a couple of really tough groundcovers. Consider Bishop's Weed (Aegopodium podagraria 'Variegatum') or Lily of the Valley (Convallaria majalis). Plant them as close together as 4 inches or as far apart as 12 inches. Create a little mound of soil on the downhill side of the plant to catch water. Then they're going to need some TLC during their first season so they'll become established. Water deeply once a week; because the water will run right down the slope, you might put a sprinkler with a fine droplet size on the site for an hour. Both Bishop's Weed and Lily of the Valley can be aggressive once they're established, and they'll be able to prevent erosion.