Is it at all possible to create a self-signed certificate for use on multiple machines on a local network which would stop the browser complaining it is not a trusted site?

We have a product which is basically a computer running lighttpd to serve a web interface for configuring the computer (sort of how a router has a web interface). There can also be many of these machines running on the same network with dynamic IP's. What I basically want to do is enable SSL for extra security but I don't want people who are on the local network to be given a browser warning about the certificate not being trusted.

Is this at all possible?