Kids go through bikes fast. My four year old's bike lasted one year before she started looking like a circus bear when she rode it. It's an expensive enough hobby for adults; for kids you're pretty much losing money from the very start. Decent bikes are expensive, and if you try and buy secondhand you're limiting your options to what's available--if the only 16" boy's bike you find is green, you're getting a green bike, so tough shit, kid.
This Instructables article walks you through a step-by-step process of stripping and repainting a bike, with clear descriptions of each steps and photos of the procedure. The commenters weigh in below the instructions with their own experience and pictures, so be sure to read through before you begin for more ideas and inspiration--a bike remodel can mean more than just a color change.
Instead of having Santa bring the latest cartoon character shilling bicycle this Christmas, why not find a solid pre-owned bike and customize it to your child's taste and interests? Why not take the hand-me-down edge of a bike that's being passed to a younger rider by tarting it up with new paint and accessories?