Not a perennial, but white sweet alyssum (Lobularia maritima) might work. It is an annual but it reseeds with abandon for me (I sprinkled seeds once a couple of years ago and it keeps coming back) and flowers constantly from early summer until we get a deep freeze. It also smells lovely and attracts butterflies. I used it as an edging last year (sorry for the poor photo quality - there are better ones in google images).

@arlene_82 Excellent idea! I've heard great things about snow princess sweet alyssum. I'm going to pick some up. It's the perfect solution. Thank you.