I have an UIPickerView inside an UIActionSheet and have done that in a way suggested by many others here at SO:
Add UIPickerView & a Button in Action sheet - How
As the comments above point out, the UIActionSheet is not designed to be subclassed or take other views.
More info here at Apple:
https://developer.apple.com/library/ios/documentation/uikit/reference/UIActionSheet_Class/Reference/Reference.html#//apple_ref/doc/uid/TP40006801-CH3-DontLinkElementID_2
One approach is to look closer at the DateCell sample code and change that to use an UIPickerView instead:
https://developer.apple.com/library/ios/samplecode/DateCell/Introduction/Intro.html#//apple_ref/doc/uid/DTS40008866-Intro-DontLinkElementID_2