I have several inputs which trigger JQuery UI datepickers e.g.
Jquery UI custom download allows you to add a custom prefix to your theme, say you added a prefix ".datepicker_wrapper" you can add this class to your datepicker this way :
$('.datepicker').datepicker({
beforeShow : function(){
if(!$('.datepicker_wrapper').length){
$('#ui-datepicker-div').wrap('');
}
}
});