We are trying to install one copy of phpmyadmin on our server so that a couple sites can login to the same copy of phpmyadmin and manage their databases. The phpmyadmin site does not talk much about this. Has anybody been able to do this?

This can be done. You will need to read the docs included with PHPMyAdmin and setup the multiple database login option. You will also have to refer to the MySQL docs for specific details. The specifics on doing this is kind of lengthy to post here. This will allow you to install a central copy of PHPMyAdmin on your server and will allow each Domain to access their DB only, using their login and password.