After you colour one cell, select another cell and press F4. That will only work, though, if you haven't done much else in between.
Could you leave the colouring until later and then select a cell of your (colour) choice and double-click the Format Painter and then click or click/drag over all the other cells you want that colour?
I know neither of those suggestions is just what you were after, but just trying to offer something since I don't think there is a keyboard method for what you want.