Restrict specific events to logged-in users

We have recently set up a members only area of our site where users have a WordPress login to access specific content on the site. I want to create some events that are visible only to those logged in users. I have tried to workaround this by installing various plugins to restrict the events content to these users however in all incidences the event title, date and venue still show in the Events list, even though the specific detail doesn’t show when the event is clicked on. Is there a way to hide these events from the calendar completely until a user is logged in?
We’re currently using the free plugin.