The default background color is black. How can I change the color, similar to tintColor
for navigation bars?
I'm pretty sure this is not possible. You may be able to work something out if you subclass it.
EDIT: I took a look at the UIMenuController.h file and there don't seem to be any obvious ways to change the color. It is a subclass of NSObject if that helps you. Also, if you take a look at how people subclass UITabBarController to change it's color you may be able to work out a similar solution.