The Ti.UI.Picker type PICKER_TYPE_DATE_AND_TIME is currently an iOS only feature.
We should add support to Android for parity with iOS.
Android does natively support a date-only and time-only pickers. Just not both.
Use a horizontal layout to contain to clickable labels. The left-aligned label will display the date and the right-aligned label will display the time. When tapping on them, their respective native date or time dialog will appear.
[ [DateLabel] [TimeLabel] ]