Go to the system view, with SM mode on, and select Earth, then click "Create new race", and create a rebel faction. It will probably need to be a player race. Then establish contact with the main empire, delete the population the game created (with the "Abandon" button in the population and production screen), and transfer Eris to the rebels. Additionally, you may have to create an empty rebel colony on Eris before you can transfer.
I haven't actually done this before, so I'd recommend backing up the database before starting.