Plugin: Set Appointments

I am trying to build a site for a friend of mine who is a personal trainer and he wants a place where his clients can go online and book available time slots for sessions. When it’s booked, the spot would be blocked off. Or the trianer could lock up times if he had prior engagements. Is anything like this possible w/ WordPress? I’ve found online schedule software but I can’t find anything that I can incorporate with WordPress.