Here's the sample from the question modified to disable the button once clicked:
$(function() {
$("#dialog").dialog({
bgiframe: true,
height: 'auto',
width: 700,
show: 'clip',
hide: 'clip',
modal: true,
buttons: {
'Add to request list': function(evt) {
// get DOM element for button
var buttonDomElement = evt.target;
// Disable the button
$(buttonDomElement).attr('disabled', true);
$('form').submit();
},
'Cancel': function() {
$(this).dialog('close');
}
}
});
}
Also, the following question will also be helpful with this: How can I disable a button on a jQuery UI dialog?