You have to step some views deeper:
let subview = actionController.view.subviews.first! as UIView
let alertContentView = subview.subviews.first! as UIView
alertContentView.backgroundColor = UIColor.blackColor()
And maybe you want to keep original corner radius:
alertContentView.layer.cornerRadius = 5;
Sorry for the "Swifting" but i'm not familiar with Objective-C. I hope that's similar.
Of course it's also important to change the title color of the actions. Unfortunately I don't know, how to set the color of actions separately. But this is, how you change all button text colors:
actionController.view.tintColor = UIColor.whiteColor();
EDIT:
The corner radius of the UIAlertController has changed since this answer's been posted! Replace this:
alertContentView.layer.cornerRadius = 5;
to this:
actionContentView.layer.cornerRadius = 15
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