Adding this PHP snippet to the functions.php of your wordpress theme will force your custom post type to be private by default. Do not forget to change my_post_type to the name of your custom post type. This is a slight change from the source snippet and does not include a password since this is private and not password protected.
if ($post['post_type'] == 'my_post_type')
$post['post_status'] = 'private';