I paint GC controllers and sell them (paid for an entire quarter of living expenses for college that way, once ^-^)
You have to get a tri-wing screwdriver (need to order it from playasia.com, or look for it on amazon, etc) because normal screwdrivers will not work. After that, take apart the controller and put the pieces immediately in a clean ziploc bag. If dust particles collect (and they can within seconds) on the circuitry of your controller, it runs the risk of ruining it.
Next, paint the controller and make sure you're using an ACRYLIC paint
NOT ENAMEL. I suggest letting each layer dry for 3-4 hours in a safe place (not in direct sunlight) and after that, when you put on the final clear coat (applications of this can happen every 30 minutes) let it dry for a full 24 hours.
Pull out your plastic ziploc bag at that point, and carefully put the thing back together. Do not get your fingerprints on the actual circuitry as this may also ruin the functionality of the controller.
Hope that helps. If you have any other questions, let me know
EDIT:
Oh, and as far as painting a Wii, I haven't tried that but I would imagine it would be much more difficult to keep dust from getting on the important parts of THAT. Same rules would apply, though I would professionally advise against it until you can get the guidance of someone who really knows what they're doing when it comes to modding or painting Wii's.