Module hook_block implementation

You can use PHP code (the expert mode) to make this "easier". Set the 'Show block on specific pages:' to 'Show if the following PHP code returns TRUE (PHP-mode, experts only).' and add the code below to 'Pages'. The code starts with the current menu item looking for a menu item with the desired path walking backwards till it finds a match (or runs out of parents). You will need to set $desired_path to the approriate value. And a word of WARNING bad PHP code can mess things up. If you want to play around with the code I suggest making content of type page, setting input format to PHP and fine tuning the code there.

// Set this to the path of the menu item 
// you want to base visibility on

$desired_path = 'node';

// We assume we do not want to show the block
$visible = FALSE;

// Get the current menu item id
$mid = menu_get_active_item();
while ( $mid ) {
   // Get the menu item
  $item = menu_get_item($mid);
  // Is the path the one we want?
  if ( $item['path'] == $desired_path ) {
    // Yes
    $visible = TRUE;
    // Found what we want, jump out of the loop
    break;
  }
   // Path not found look at the parent menu item
   $mid = $item['pid'];
}

return $visible;