|I'm sure the black or gray market can supply what you need. |
In the U.S. you can grab a prepaid phone at the local convenience store, it's just like a prepaid VISA. You use it until you run out of prepaid minutes and either replenish it or toss it when you're done, no questions asked.
So just make sure your face isn't visible to the convenience store security cameras when you buy the phone and you're good.