I went to the #wordpress irc channel and was given the answer by Marko Heijnen. He grabbed the Walker Code from /wp-includes/post-template.php and added a few lines to it.
/**
* Extend the default page walker class to append class names for pages that
* are parents.
* @uses Walker_Page
*
* http://wordpress.stackexchange.com/questions/11821/class-parent-for-wp-list-pages
*
*/
class My_Page_Walker extends Walker_Page
{
/**
* Filter in the classes for parents.
*/
function _filterClass( $class )
{
$class[] = 'parent'; // change this to whatever classe(s) you require
return $class;
}
/**
* This is effectively a wrapper for the default method, dynamically adding
* and removing the class filter when the current item has children.
*/
function start_el( &$output, $page, $depth, $args, $current_page )
{
if ( !empty($args['has_children']) )
add_filter( 'page_css_class', array( &$this, '_filterClass') );
if ( $depth )
$indent = str_repeat("\t", $depth);
else
$indent="";
extract($args, EXTR_SKIP);
$css_class = array('page_item', 'page-item-'.$page->ID);
if ( !empty($current_page) ) {
$_current_page = get_page( $current_page );
_get_post_ancestors($_current_page);
if ( isset($_current_page->ancestors) && in_array($page->ID, (array) $_current_page->ancestors) )
$css_class[] = 'current_page_ancestor';
if ( $page->ID == $current_page )
$css_class[] = 'current_page_item';
elseif ( $_current_page && $page->ID == $_current_page->post_parent )
$css_class[] = 'current_page_parent';
} elseif ( $page->ID == get_option('page_for_posts') ) {
$css_class[] = 'current_page_parent';
}
$css_class = implode(' ', apply_filters('page_css_class', $css_class, $page));
$output .= $indent . '<li class="' . $css_class . '"><a href="' . get_permalink($page->ID) . '">' . $link_before;
$image = get_post_meta($page->ID, 'title_image', true);
if ( isset($image) && !empty($image) ) {
$output .= '<img src="'. $image .'" alt="'. apply_filters( 'the_title', $page->post_title, $page->ID ) .'" />';
}
else {
$output .= apply_filters( 'the_title', $page->post_title, $page->ID );
}
$output .= $link_after . '</a>';
if ( !empty($show_date) ) {
if ( 'modified' == $show_date )
$time = $page->post_modified;
else
$time = $page->post_date;
$output .= " " . mysql2date($date_format, $time);
}
if ( !empty($args['has_children']) )
remove_filter( 'page_css_class', array( &$this, '_filterClass') );
}
}