Search child pages from a specific page parent

Question

Anyone know of an easy way to alter the default WordPress search from searching ALL pages, to searching only child pages from a specific page parent?

I know of the filter you can use to alter whether pages or posts are searched:

function SearchFilter($query) {
if ($query->is_search) {
    $query->set('post_type', 'page');
}
return $query;
}
add_filter('pre_get_posts','SearchFilter');

Maybe there is a way to add further information here to specify a particular page parent?

Answer 1

I have no idea if this will work, but couldn't you reference the post_parent in the query args?

function SearchFilter($query) {
if ($query->is_search) {
    //$query->set('post_type', 'page');
    global $post;
    $query->set( 'post_parent', $post->ID );
}
return $query;
}
add_filter('pre_get_posts','SearchFilter');

Again, completely untested. I'm not terribly familiar with using $query->set().

Answer 2

Chip's answer works fine for me. (Sorry, I have like zero reputation so cannot vote up or comment...)

I'm actually using it for displaying only search results on a specific template:

function SearchFilter($query) {
    if ($query->is_search) {
        //$query->set('post_type', 'page');
        $query->set( 'meta_key', '_wp_page_template' );
        $query->set( 'meta_value', 'template-content.php' );        
    }
    return $query;
}
add_filter('pre_get_posts','SearchFilter');