For some unknown (by me) reason WinJS.UI.DatePicker is only available for Windows Store apps, not Windows Phone. (the control is also available for XAML apps).
The suggestion is have an input element, which I believe is awful. I also googled around for a cool Date picker but of course there are tons of controls for JavaScript but most of them are not touch oriented, and frankly the touch oriented controls I found were not very Windows Phone-like. So I decided to create my own DateTime picker.
It's a very simple control which basically adds a select for every "part" of the date. Which means one for the day, one for the month, and one for the year.
This does not pretend to be a full featured control, it just meet my own needs, but I'll be glad to take pull request if you feel like contributing.