Placing favicon.ico in the root of your domain only really affects IE5, IIRC. For more modern browsers you should be able to include a link tag to point to another directory:
<link rel="SHORTCUT ICON" href="http://www.mydomain.com/content/favicon.ico"/>
You can also use non-ico files for browsers other than IE, for which I'd maybe use the following conditional statement to serve a PNG to FF,etc, and an ICO to IE:
<link rel="icon" type="image/png" href="http://www.mydomain.com/content/favicon.png" />
<!--[if IE]>
<link rel="shortcut icon" href="http://www.mydomain.com/content/favicon.ico" type="image/vnd.microsoft.icon" />
<![endif]-->