If you are an admin you can see the latest PM with a similar link http://your-site.com/private-posts.rss It’s not accurate but you can see if a particular user send more PM in a day.
Or you can run a query to have a list of users and PM in the last X days (you need to install Data explorer plugin).
Something like this SQL query to get the queue of all the PMs in the system is a good start point to write your own query.