I got my Easy Post Types datepicker working by changing the plugins/easy-post-types/classes/custom-datefield/custom-datefield.php file to have a call to 1.7 instead of 1.8 (it is almost the last line):
wp_enqueue_style('custom-datefield-style', 'https://ajax.googleapis.com/ajax/libs/jqueryui/1.7/themes/base/jquery-ui.css');