If you have a paid account and want to override the default favicon on your journal, it's fairly easy.
1. Find or make a 16x16 graphic you like. p.yusukekamiyamane.com's Fugue and Diagona sets are good, quick options free for use on non-commercial sites.
2. Convert your graphic to .ico. If your icon is .png, you can use this site. Otherwise, just Google, online converters are easy to find.
3. Host your image somewhere that allows hotlinking.
4. See this tutorial.
Please note that this override will not show in IE or Chrome. I've also tested it in Firefox and Opera, however, and it works for those browsers. You can see my personal journal (bzzinglikeneon) for an example.