re-register custom post type with custom capabilities

Have you tried something like this:

'description' => __( 'This is where you can add new Connectors' ),
'public' => true,
'show_ui' => true,
'capability_type' => 'page',        
'publicly_queryable' => true,
'exclude_from_search' => false,
'hierarchical' => true,
'capabilities'        => array(
'publish_posts'       => 'update_core',
'edit_others_posts'   => 'update_core',
'delete_posts'        => 'update_core',
'delete_others_posts' => 'update_core',
'read_private_posts'  => 'update_core',
'edit_post'           => 'edit_posts',
'delete_post'         => 'update_core',
'read_post'           => 'edit_posts',
),
'rewrite' => array( 'slug' => 'connector', 'with_front' => false ),
'query_var' => true,
'supports' => array( 'title', 'editor', 'thumbnail', 'comments', 'excerpt','author',/*, 'page-attributes'*/ ),
'taxonomies' => array('post_tag'), // this is IMPORTANT for adding tags
'has_archive' => true,
'show_in_nav_menus' => true,
'show_in_menu'=>false
));