I have modified @skafandri answer to avoid re-apply the datepicker constructor to all inputs with .datepicker_recurring_start class.
Here's the HTML:
<div id="content"></div>
<button id="cmd">add a datepicker</button>
Here's the JS:
$('#cmd').click(function() {
var new_datepicker = $('<input type="text">').datepicker();
$('#content').append('<br>a datepicker ').append(new_datepicker);
});
here's a working demo