If you update your favicon, it might not appear in the Safari browser because the "old" version ist still in the cache of the browser. Favicons have a long and very strange history, and you can clear Safari's cache by following these steps: 

  1. Quit Safari.
  2. In the Finder, select Go > Go To Folder.
  3. Enter ~/Library/Safari/Favicon Cache/ and press Return
  4. Use Select All (Command-A) to select the database and cached items.

5. Drag these to the trash or press Command-Delete.

6. Empty the trash.