RSVP Pro (our gold member event registration addon) can do this out of the box - though you may want to use CSS to modify the styling to suit your site's appearance.

You would need to set up 2 series of daily repeating events (one for am and another for pm) with a registration limit of 12 (a new series starting each month may be a good idea to make it easier to change prices etc. You can capture custom information in the registration form. When full the event would show that the registration is full or it could be hidden completely. Also with JEvents it would be easy to remove specific repeats occuring on public holidays etc. if required.