Create a sign-up calendar and workflow for WordPress site

We are in need of a sign-up calendar. We would like the calendar to display in month views, with one sign-up button on each day. When someone would like to sign-up for a day, they click the button and a short form pops up. Similar to a contact form, the information they provide would be emailed to me. I would approve them on the desired day, and the sign-up button would disappear and be replaced with their name. A similar calendar can be found here: [login to view URL] This will need to be developed for a wordpress site.