Hi Jack,
I think that would be a big ask. WindJack Solutions (http://windjack.com/) have a great tool for developing dialogs, AcroDialog, however it does not include a date picker.
Thom also has a subscription service (http://www.pdfscripting.com/) which has some solutions for Javascript date pickers.
Overall I think that it would be very difficult to implement in a dialog.
Good luck,
Niall
Assure Dynamics