I ran into this site with a picture to favicon generator. No software download, just works within the webpage. Plus they have a huge archive of favicons there. As you can see (or actually not anymore) this site needed a new one badly :) The default Joomla one was still hanging in there.
Oh and I also found out, when replacing Joomla favicon, you have to upload it to the /images directory on your server, not just in the root as in normal websites.
