A favicon (short for favorites icon) is a 16×16 pixel square icon with .ico extension and now you may use your own favicon in your Google site rather then Google Sites default favicon. Note: The favicon file name must be "favicon" and extension must be ".ico" means the favicon file will "favicon.ico".
Click at "More action" and then click "Manage site".
Click "Attachments" from the left panel under "Site settings" and then click "Upload"
When you click "Upload", a box will appers and browser the favicon.ico file and click "OK". Note: The "favicon.ico" file must be at "top level" i.e. / level.
Verify that "favicon.ico" file, you will see in "Attachments" that it has been uploaded at the top level i.e. " / ".
Congratulation, you have changed the default Google Sites favicon with your own favicon.
To verify: open web browser and type "[your site URL]/favicon.ico" and go! For example, www.siteshelp.com/favicon.ico or simply open your site in web browser.