^this is the answer if it's communication between lots of different users and the admin that you want to keep discussions private from others. I interpreted the OP's post due to how it was written as between a single user and an admin.
Just make sure that it's set for unregistered too. I had my "contact" forum one-on-one with members for the first 2 months, so I thought, but if you logged out, you could see all posts.