This is code that will allow the use of Christian Varga's handy WordPress auto-submenu code.

Genesis Auto Submenu

/** dave's genesis code for making the submenu  **/
add_action( 'wp_head', 'dc_add_tricky_menu' );
function dc_add_tricky_menu () {
	// make all menus one level, or else dropdowns will be redundant in your submenu.
	add_filter( 'wp_nav_menu_args', 'my_wp_nav_menu_args' );
	// stick submenu under main menu. Of course you can use other hooks to put menu & submenu elsewhere.
	add_action( 'genesis_after_header', 'dc_add_tricky_two' );
}

function my_wp_nav_menu_args( $args = '' ) {
	$args['depth'] = 1;
	return $args;
}

function dc_add_tricky_two () {
	// this code is for retaining styling from the main menu, but giving you a class to re-style the menu if desired.
	echo '<nav class="nav-primary submenu" role="navigation" itemscope="itemscope" itemtype="http://schema.org/SiteNavigationElement"><div class="wrap">';
	wp_nav_menu( array(
  		'theme_location' => 'primary',
		'container' => 'false',
  		'menu_class' => 'genesis-nav-menu',
  		'sub_menu' => true
	) );
	echo '</div></nav>';
}
/**** end of dave's submenu code ****/