Is your chosen paint (or possibly dye) suitable for painting plastics? Is said paint likely to take wear? is your paint poisonous on contact (probably not but there are some that contain rat, fish or plant poisons)? Are you planning to treat the surface of the GBA are painting or are you up for a layer of primer/undercoat? Do you have spray gear or is this brush and dipping only? You do know you can get vinyl wraps for such things right and truly custom ones are not the most expensive?
There are many many ways to colour plastics of different sorts (not sure what the various GBA shells use offhand and I would rather not disassemble one right now, the DS has some ABS on it though.