Google Texas AM cooperative extension service and search for 2x2 foot evergreen plants. Architects are no friends to gardeners when they put such narrow planting box on a house. Another thought, travel around the neighborhood and see what others have done, good and bad.

Oh, thought I was in the Texas forum. Google Cornell or Rutgars extension service and ask the same question.

Boxwood will work :-) Grows very slowly, is pretty darn hardy and will be a year round presence. Since these types of planters are generally tucked under the eaves of the house or roof overhang, make sure you pay attention to watering. And make sure there is decent potting soil in the planter and fertilize periodically.