Unfortunately it's not possible to backlight a GBC. You have to front light it which, IMO, is not a fantastic way to solve the issue. The best way to play backlit GBC games is to pick up one of the backlit original GBAs from Rose Colored Gaming (albeit an expensive option, depending on your gaming budget).
If you're interested in an original backlit GB, I think I have everything I need to make one or two more at the moment.