Can CA server generate generic site certificate

Thanks to all in advance for your help.

The multi-function printers in my office need to be protected by SSL
certificates. I had considered using self-signed certificates but don't want
my users worrying about the warnings the new versions of the browsers are all
displaying. Each MFP could generate its own Certificate Signing Request,
which I could then use to generate an SSL certificate for each device, but
that sounds like a lot of work.

I am wondering if I could generate a "generic" certificate and install that
to all the devices. Since it would be tied to our CA server which is already
trusted by all my users, my problems would over.

Any thoughts?

Nikko