I need a booking system for a theoretical project website. It would be an in-house job (not outsourcing to a web service) but all google searches on the subject yield results for said web services.

I'd want to be able to use the system as such: For each day, there is availability recorded and if available a user can book in using the website, which sets that date to unavailable. There are other complexities, but this is the basic system I am trying to achieve - what would allow me to implement something like this?