Okay, so where do you manage your DNS? Wherever that is, create your domain or sub-domain and point its "A" record to the same IP address your main domain "A" record points to.
At this point, open IIS, select the website in question and click the "Bindings" link in the Actions pane. Click the Add button, and enter the domain.
Now, go to the Site Settings for the child site and click the "Host Name Mappings" tab and enter the domain there.