kupidon,
для изменения, кликнуть по дате, выбрать нужную в календаре.
<!DOCTYPE html>
<html>
<head>
<title>Untitled</title>
<meta charset="utf-8">
<style type="text/css">
</style>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.12.4/jquery.min.js"></script>
<link rel="stylesheet" href="https://ajax.googleapis.com/ajax/libs/jqueryui/1.11.4/themes/smoothness/jquery-ui.css">
<script src="https://ajax.googleapis.com/ajax/libs/jqueryui/1.11.4/jquery-ui.min.js"></script>
<script>
$(function() {
$("td.edit").on("click", function(event) {
event.pageY +=18;
var self = this;
$({}).datepicker("dialog", self.innerHTML, function(data) {
$(self).html(data)
}, {
dateFormat: "dd.mm.yy"
}, event)
})
});
</script>
</head>
<body>
<table>
<tr><td class="edit payment_date 44380">11.11.2016</td></tr>
<tr><td class="edit payment_date 44381">12.11.2016</td></tr>
<tr><td class="edit payment_date 44381">13.11.2016</td></tr>
</table>
</body>
</html>