You would need to have somebody that knows what they are doing with PHP (what this forum runs on) or ASP to code up a website. You would then need to host it on a server along with a database such as SQL Server or MySql.
I recommend going with PHP and MySql as they are open source so you do not have to pay a licensing fee. There are numerous resources on the web, and there might even be something pre-programmed close to what you're looking for.
Another option is to have each member setup and maintain a Google calendar at
http://calendar.google.com and have them share the calendar with the AD or assigner. This probably isn't the most streamlined way of doing things but it is free and easier to setup (don't have to deal with security settings, etc).
The other option is going with assigning software such as The Arbiter, Ref Town, Zebraware, etc. My association uses the Arbiter where I can block off my availability, be assigned games, see who I am working with and our assigner can post messages for the association to read.