My favorites for that kind of situation are creeping thyme and Roman Chamomile. Neither minds foot traffic much. There is a nursery called Steppables which specializes in foot-traffic tolerant groundcovers for all sorts of climates and conditions. Their website is a fount of excellent ideas for this! You might be too wet for wooly thyme, for instance; you might not have enough sun for chamomile, etc. They only sell by the flat, and I can never afford to buy that much plant material at once, but perhaps you can. If not, you can at least discover which groundcovers you'd like to experiment with.
There is also low-growing white clover, which I saw seeds for recently -- was probably either Territorial Seeds or Johnny's Seeds. They were advertising this clover as a ground cover in particular. Seeding instead of setting out plants would mean you'd need to out-compete bird seedeaters though.