Try some Ipomoea vine. Comes in many colors (mostly purple or chartreuse). It's avaliable widely at nurserys and home centers.

You could try lobelia. It would trail over the sides and make quite a color impact with the blue/purple against the white house.

Another wonderful shade windowbox flower is coleus. It doesn't trail though.

I have used ipomoea in full sun containters previously and I thought it was a sun loving plant. Will it do ok in a shady windowbox?

Certain varieties of coleus will trail at least a bit and even upright varieties will billow a bit if pinched back. It seems the deeper the shade the more they have trailing tendencies. Mine are in deep shade with only morning light and always fall below the rim of the pot, drooping down 2 feet or so.

Elephant ears, aspargus fern, bacopa, and fibrous begonia are also options.

I've had good luck with Swedish Ivy in my shaded window boxes. Trails beautifully. This plant also comes in a varigated version.