You can allow Site Owners to create sub-sites under a site they own. Of course, you can decide if they can or not - and if they can you can give them a curated list of Service Definitions they can select from. Any sub-sites created follow the standard site-creation process, which means all the settings (branding / approval / security...)for that Service Definition are applied, and the site will appear in the directory.
To allow a Site Owner to create a sub-site at all, you must enable the action in the Actions tab. See Managing Actions.
To build a list of approved sub-sites the Site Owner can choose from, navigate to the Sub Sites tab in the Service Definition you're editing:
You'll then see a list of all Service Definitions. Clicking on one will turn it green to indicate it's selected. You can select as many as you like:
Note: Since a sub-site is another Service Definition, all the same rules apply. For a user to see it, they must be in the security list for it, and the Service Definition must be active.