The only way I've found to quickly password-protect the archive is by creating a template that retrieves the custom post type data and associating it with a page that can be password protected.
http://codex.wordpress.org/Page_Templates
Once that page is password protected, you find the post ID to apply it to the single-{your_custom_post_type}.php like so:
<?php
if ( !post_password_required('{protected_post_id}') ) : ?>
//protected content here
<?php else:
//show the password form of the protected page
echo get_the_password_form('{protected_post_id}');
endif; ?>
This saves you from having to password-protect every post under your custom post type.