The following can be added to a site specific plugin or through a child theme's functions.php file.
<?php
//* Do NOT include the opening php tag
//* Add noindex nofollow to the Event Espresso event listings page
function ee_noindex_nofollow_event_listing_page() {
if( is_post_type_archive('espresso_events') )
echo( '<meta name="robots" content="noindex,nofollow" />' );
}
add_action( 'wp_head', 'ee_noindex_nofollow_event_listing_page' );
References: