There are a few ways to do that.
One method is to select the area, then add a Hue/Saturation adjustment layer (which, at least here in PSE10) is automatically masked to your selection. In the H/S layer settings, use the "Colorize" option. For white areas you need to move the Lightness slider to the left (darker) for the colour you've chosen to show. Similarly, for the black areas, move the Lightness slider to the lighter side.