I see the datetimepicker does not have 'DataSource' and 'DisplayMember' properties.
I don't think they make sense for the date time picker. There's probably a few ways you can define them for the control, but I can't think of any that make a date time picker the better choice than a combo box or some other aggregate control except for what the date time picker does now without those two properties.
Would it very difficult to add these properties?
I don't think so, but you'd have to do a lot of micromanagement to make sure that only the data source dates can be selected by the calendar dropdown or spinners.