Allow users (or only some users? could require a new capability) the option of creating user events that are "shared" with other users. Like the ability to send and accept appointments in Novell Groupwise.
The user creating the event would select other users on the site to share the event with. This could be configurable to only allow appointments to be shared with certainly users, e.g. teachers or coursemates.
The event would be created on the first user's calendar, as a user event.
A message would be sent to all users the event is being shared with, including a link for them to accept the event. When they click the link, the event is created on their calendar as a user event.
Discussion thread here: http://moodle.org/mod/forum/discuss.php?d=136930