Bill
Yes, you can do this, though it's a manual procedure.

First, create the directory under the website root that matches the name of the child portal : ie example.com/childportal -> create a directory called 'childportal'.
Next, copy in the /default.aspx file that is created for child portals.  If you don't have a copy of this file anywhere, just create a child portal, and copy out the file when it is created.
Finally, add in example.com/childportal as a portal alias for the child portal through the site settings.

Restart the application through host settings and example.com/childportal should now work (asuming this install already has example.com setup as a parent portal)

If it's an existing, search indexed site you will want to setup a 301 redirect from the old domain to the new domain + child portal so that existing users and search engines pick up the new location.  You will also want to check the html throughout the site in case you have some links that don't work after you change the domain name and path of the portal.