Registration and Hosting are two separate deals. Do you have a free registration credit laying around? I have multiple domains registered here, but only one gets the free renewal because it’s on the same renew date as my hosting plan. The others I have to pay for as they come up because I don’t have that registration credit sitting idle. Also, there’s no coupon for domain registration. It’s $9.95 for anybody.
For the website, will you be hosting it on your plan? With unlimited domains and all the space they give us, it’s not going to use a significant amount of space. The domain can be registered anywhere just as long as the registration is configured to use DreamHost’s name servers. He can even create his own WebID so he can register his domain here, then let you set up the actual hosting under your account.