In CivilizationIII\Art\Civilopedia\Icons you'll notice government icons - anarchy and despotism. These icons are referenced in pediaicons.txt. So find some nice icons that represent your gov and drop them in that folder, then write an entry for it in pediaicons. You can use the other GOVT_ entries as template.
Please see the enclosed zip for icons on Republic ('empire'), Democracy, Fascism and Robotopia. The democracy one is just a copy of the tech icons for the Democracy advance.