You should be able to add both public and private repositories on GitLocalize. If, however, the private repository you wish to add is part of a GitHub organization, you will need to have the Owner role in that organization in order to add it.
If you do not see your private repository in the dropdown list of available repos, please check your permissions in the GitHub organization or ask an organization owner to add your project for you.
This is due to the way our GitHub app is granted access to repositories that are part of an organization.
Projects added for private repositories are also private.