There is this code in header.php:
<link rel="stylesheet" type="text/css" href="<?php bloginfo('stylesheet_url'); ?>" />
<link rel="stylesheet" type="text/css" href="<?php bloginfo('stylesheet_directory'); ?>/styles/white.css" title="white" />
<link rel="alternate stylesheet" type="text/css" href="<?php bloginfo('stylesheet_directory'); ?>/styles/black.css" title="black" />
<link rel="alternate stylesheet" type="text/css" href="<?php bloginfo('stylesheet_directory'); ?>/styles/blue.css" title="blue" />
<link rel="alternate stylesheet" type="text/css" href="<?php bloginfo('stylesheet_directory'); ?>/styles/green.css" title="green" />
<link rel="alternate stylesheet" type="text/css" href="<?php bloginfo('stylesheet_directory'); ?>/styles/grey.css" title="grey" />
And all you need to do is switch /styles/white.css with styles/black.css, as well as switching the titles. That way black is at the top, and white is an ‘alternative’ stylesheet.