The Private Media Channel gives you an option to take a report of all the emails sent in your channel. In Analytics > Email Log Report you can generate the report that gives you details of the sender's name & email, receiver's name & email, and the subject of the email. Most importantly it gives information about the event in the channel that triggered the email and the community and content in which the event took place. Last but not the least it gives an account of the status of the email sent to the user.
Ain't this cool. Now all you have to do is click on the 'Export Report' button in the top right-hand corner of the page and you have an excel report of the email log from your channel.