Black background on iPhone 4?
Create a black image in your favorite image editor (even Paint will do if you're on Windows), save it as a jpeg, and e-mail or sync it to the phone. Then set that image as the background. 

Since you're making it all black, I doubt the resolution is going to matter much, but you can always use 960 x 640 to use the iPhone 4's standard resolution.

Edit to add a black image that works: