Unfortunately, what you need to do is EITHER:
Choose the bone that you want to ADD WEIGHTS TO, and start white-painting with THAT bone instead of black-painting with the other bone. The vertex-painting can't delete weight, it can only add or REPLACE weight, which brings me to...
In the Paint Skin Weights tool (click the box to the right of the Skin Weights menu item), change the type of paint to Replace instead of Add, and then set the Value to 0. This will ELIMINATE all weight given to the vert by the selected bone. Now if you want, you can set the Value to anything you want, and it will replace the existing value with the Value you choose. (Be sure to switch back between Add and Replace, or you'll be hitting your Undo button a lot
)