Adding to Justin's answer, if you're worried about untidy markup or you don't want this value hard coded in CSS you can set the input before it is shown. Something like this:
$('input').datepicker({
beforeShow:function(input){
$(input).dialog("widget").css({
"position": "relative",
"z-index": 20
});
}
});
Note that you cannot omit the "position": "relative" rule, as the plugin either looks in the inline style for both rules or the stylesheet, but not both.
The dialog("widget") is the actual datepicker that pops up.