Is there a way to have clients request a time and then have that time slot not appear?

If I make a form for customers to reserve a time for a photo session, can I then have that time slot no longer be available as an option for other customers to choose? 

You can use our appointment slots widget to accomplish this.
You can see a demo here: http://form.jotformpro.com/form/43352010062942

Check it out and let us know if it would work for you.
Thanks.