Project a solid color onto a game object

Hello,

I am trying to project a solid color onto gameobjects in order to create a cursor highlight. When I try to do this with a projector and a home made material I change the texture of the whole game object.

I would like to change the color of just the surface that intersects with the projector. I have illustrated what I am trying to highlight with the red box below.

How can I achieve this? Your help is much appreciated!