You can review our Groundcovers page and there is a drop down menu for full sun and dry conditions. Moss phlox is a beautiful native plant that flowers in the spring and stays green (sometimes turning a bronze red in colder temps). It is available in many different cultivar colors ranging from shades of pink to white to purple. It is easy to find at  most garden centers and you may even be able to get flats of it to fill large spaces. 

There are various sedum varieties as well. These would not be native but are various shades of green and some are a deep red color too. 

Some Carex or sedge species have a grass like texture and can do well in sunny locations and some are more reliably evergreen than others, most are native too. 

Let us know if you have any questions. 

Emily



You're welcome!