To change the favicon with Google sites

1. login to your site

2. click on 'More actions' (top right)

3. select 'Manage site'

4. click on 'Attachments' (left menu)

5. click on 'Upload' (top left)

6. browse to your customized favicon.ico file (16x16px) and click on 'Upload attachment to / (top level)' radio button

7. 'Return to site' and refresh

Icon creator:    http://www.convertico.com/