This instructions provided by courtesy of Arash.
To possibly help other/future customers let me tell you how we got this working on Twinkle/Ubuntu. We were using the default Twinkle package that comes with Ubuntu, which is version 1.2 not the newer version 1.4. We followed the instructions in the diamond wiki (yes I did read it) for the 'older versions' section of the Twinkle instructions. That got us to being able to call out etc but not receive phone calls.
So, I did some research and found instructions to upgrade Twinkle to 1.4 in Ubuntu here: https://launchpad.net/~gnutelephony/+archive/ppa
Basically, adding the line:
deb http://ppa.launchpad.net/gnutelephony/ppa/ubuntu jaunty main
to software sources and updating Ubuntu got it to upgrade Twinkle along with all its dependencies.
Once we were upgraded to 1.4 we deleted the old user account and added a "Diamond" account, which was a breeze and works well (including with incoming calls etc.)
Version 1.4 of Twinkle won't be part of Ubuntu until Ubuntu 9.10 in October.... so until then doing the above will help all your Ubuntu customers.