Right now your configuration is:
DNS -> Your Server
So the only point where you could do anything is by redirecting the domain:
DNS -| Your Server
|-> Some Other Server Hosting 'This is Down'
Unfortunately, DNS gets cached so aggressively that it can be quite a while before an update, either to take your site down, or to bring it back up, would propagate everywhere. A short TTL on the DNS record would help, but it would hurt performance a bit.
The best move in general is to have a reverse proxy or load balancer in front of your machine:
DNS -> Load Balancer -> Your Server
That way, you can change where the load balancer points, or even get the load balancer itself to host the 'This is Down' message. It also opens you up to a more reliable configuration, where you have more than one server:
DNS -> Load Balancer +--> Server 1
+--> Server 2
In this configuration you may be able to take only one machine down at a time, and not have your site down at all.
Your final option incidentally, if you don't need to restart the machine, or you don't mind that the site will still be down while it's restarting, is to condense all of this onto a single machine. Run Nginx on the machine, have it proxy to IIS normally, but show an error message when necessary.