The Favicon is a parameter that is generally hardcoded in a template.
You can either modify the template to provide a path that is unique for each website
OR
use the Search/Replace plugin to replace the value in the page by another location or other favicon file name.
www.jms2win.com/en/component/docman/doc_...rch--replace-utility
See the source of your page and you may have something like
<link href="...../administrator/templates/bluestork/favicon.ico" rel="shortcut icon" type="image/vnd.microsoft.icon" />
You could setup the Search/Replace plugin to mention for example
favicon.ico=favicon_site1.ico
or
totally change the path and provide a new path.
/administrator/templates/bluestork/favicon.ico=/images/favicon.ico