Custom login Image for each site in Multisite installs


Playing with Ultimate Branding I've added some custom CSS to the login page.
However, I'd wanted to go one step further and use Wordpress's custom classes to even customize login-image for each of my sites (a multisite install).

The default login page has this code in it:

<body class="login">

What I wanted is to be able to add a custom class for the body tag. Like this:

<body class="login mycustomtext">

For posts and pages it's very easy since I'm using Genesis Framework (from Studiopress). But, for the login page...??? Is it possible to achieve it?

Thanks in advance.