Is there an option for users to set their availability?

The short answer is not yet.

I plan on adding this feature within a few weeks because I know that it is a big deterrent not having it.

As a temporary solution, here is what I will do and recommend.

I will add another permission to the final version of 1.0 for a user to be able to edit an unpublished schedule.  Give your user group and all your users that permission along with the permission to be able to view unpublished schedules.  Create the schedule a head of time and notify your users.  They will then be able to login and edit the schedule according to their needs.  The scheduler/supervisor can then login, review the schedule, make changes and publish it.  Users will not be able to edit the schedule after it has been published unless you have given them permission to do so.

The final 1.0 version should be released within a couple days.