How can I add the ability for a user to add/edit administrators?

Make sure you’re adding and removing roles on plugin activation/deactivation.

add_role() only adds a role if it doesn’t already exist. So if you already added the developer role without the capability to add administrators, calling add_role() again won’t re-add the role. You have to remove the role first.

<?php
/**
 * Plugin Name: Stackexchange Sample
 */

//* Don't access this file directly
defined( 'ABSPATH' ) or die();

//* Add role for developer that has the same capabilities as administrators
register_activation_hook( __FILE__ , 'wpse_106269_activation' );
function wpse_106269_activation() {
  $admin_role = get_role( 'administrator' );
  add_role( 'developer', __( 'Developer' ), $admin_role->capabilities );
}

//* Remove developer role
register_deactivation_hook( __FILE__ , 'wpse_106269_deactivation' );
function wpse_106269_activation() {
  remove_role( 'developer' );
}

Deactivate and re-activate your plugin and the developer role should have the same capabilities as the administrator role.