Answer
Create a new profile, and give the user the ability to manage his own domain. Now edit the User Variables for that user under the Support menu. Select the "Domains" variable from the scrollable list and enter a space separated list of domains that this user is allowed to manage.
If you update the profile at a later date then you will need to reset this variable again so you should set up the complete profile for this user prior to amending the variable.
See also
Why is my user variables tab greyed out?
Keywords:Profile, Domain, Domains, Manage