I would recommend either Blue Skies of Mapleview (
Blue Skies of Mapleview LLC) or Bridlewood Farm (
Bridlewood Farm - Home). Both are great. They both do lessons and summer camps for girls, and Bridlewood even has an after school program for girls which picks up from the Chapel Hill schools.
The only one I do NOT recommend Spence's Farm. If you're wondering why, just search on their name and look for the article from IndyWeek.
HTH.