Coinbase owns Coinbase addresses.  They agree to credit your account and allow withdrawals, but they maintain control of 100% of the bitcoin addresses they use.  If you want to sign messages, you have to create a new bitcoin address that you control the private key to.  Then, you can sign messages like the Eligius message.  Make sure you understand this before you do it, as you will have to manage your BTC address and payments.  Also, Elgius uses coinbase (small c) payments, which many exchanges and brokers have trouble with, so I wouldn't use a Coinbase (large c) address with any mining pool.