When I had my 1st Gen. iPhone, I wanted to change the backing because it was scratched and dinged in some places.
Some eBayers sell the kits. I wanted to buy one, but I didn't want to risk ruining my phone.
But if you are a risk taker, go on ahead and give it a shot to change the housing to whatever color you please.
But as suggested, you can try ColorWare starting at $150. It's worth it for them to do it if you are desperate to change the color.
Good luck, 🙂