Hi Jirka,
Actually, you can just delete the favicon.ico file from Kentico CMS directory and copy your ones to each site's App_Themes folder (e.g.
~/App_Themes/CorporateSite/favicon.ico). Now please switch to the
Masterpage tab on your master page and there is a text filed between the head tags, so please fill it with:
<link rel="shortcut icon" href="~/App_Themes/CorporateSite/favicon.ico" />
and apply this approach for each site you have. Don't forget restart the application (
Site Manager ->Administration -> System) after you set these new favicons.
Best regards,
Jan Hermann