Add div wrapper below the widget title

Re-register the default genesis sidebar into your function.php. See the image above for html output.

genesis_register_sidebar( array( 
		'id' => 'sidebar',
		'name'  => __( 'Primary Sidebar', 'genesis' ), 
		'before' => '<div id="%1$s" class="widget %2$s">',
		'after'  => '</div></div>',	
		'before_title'  => '<h4 class="widget-title widgettitle">',
		'after_title'   => '</h4><div class="widget-inner">'
	)
);