You can use a third party tool to add a calendar to your site - such as Google calendar. To add a Google calendar to your site:
1) Get the code snippet to share your calendar from Google. Please see this article for instructions: https://support.google.com/calendar/answer/41207?hl=en
2) In Sites > [site name] > Pages > [page name], choose the HTML tab in the text editor and paste the code snippet into the text editor.
Just remember that in order for visitors to see the calendar, you must make the calendar public. There are instructions for this in the Google support article in step 1. There are other calendar tools that you can use, but Google is an example of one that is easy and free.