Exactly. lat9 is right. It's ugly:
You'd need to edit (nearly) all of your /admin/*.php files (but not likely the files in any admin subdirs) and search for this:
<link rel="stylesheet" type="text/css" href="includes/stylesheet.css">
and add this on a new line below it:
<link rel="icon" href="admin_favicon.ico" type="image/x-icon" />
<link rel="shortcut icon" href="admin_favicon.ico" type="image/x-icon" />
... or some variation of that.
Remember, every browser handles favicons with its own quirks, so you might need to flush cache, make bookmarks, delete history for old admin pages in your browser history, and experiment with various .ico file formats.
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