Creating Custom form that updates page – Plugin Available?

I am trying to create a form in which the user would have a selection of choices, say appointment times, and they can only select one. Once that user submits the form, that selection, or time, is no longer available to the next user.

I have tried a few plugins, but nothing has that capability.

Does anybody know how I can hack that capability? Or a plugin that will do that for me?

Thank you!