Windows 2000 and computer certificates

I've followed this Microsoft documentation to setup WLAN with eap-tls.
http://go.microsoft.com/fwlink/?LinkId=14844

This works great with Windows XP machines. I now need to add support for
Windows 2000 machines. I'm aware of the patch needed to support 802.1x
authentication on Windows 2000.

The problem is getting the certificate for the computer. Autoenrollment or
manual enrollment through MMC do not work. Does the certificate template
need to be changed for Windows 2000 two be able to enroll it?

I do receive the user certificate through the web enrollment tool on Windows
2000 machine but Computer certificates are only enrolled to Windows XP
machines.