Ed,
Cerium oxide and chromium oxide are both good polishes for beryl. Although, if you are using powder chromium oxide it will find its way into the pours of your stone, leaving it green.
My polish of choice for beryl is cerium oxide. There are a few places where you can get cerium laps as well as two different grades of cerium. LightningLap.com sells cerium laps as toppers that use the white cerium (99%). These cost around $30.00 and they work exceptionally well.
Pol-A-Gem sells standard size red cerium laps (94%) that also work quite well.
The difference between red and white cerium is that the red is a bit more coarse. But as far as polishing is concerned the finish they leave is like the difference between 100,000 and 200,000 diamond, which is very slight and only noticeable under magnification.
Gearloose sells the Greenway lap which is green in color and uses chromium. I have not tried to use it on anything but green stones, so I don’t know if it leaves any green residue on the stone.
You can also get a combo pack of ultra laps that have cerium, aluminum, chromium and tin oxide. They work well but leave a slightly rounded meet.
If you choose to use the white cerium laps there is another suggestion that I have. Covington sells a cerium spray kit which includes a spray bottle and some white cerium powder. You put a measured amount of cerium powder in the bottle, add water and shake before spraying it on your polishing lap. Gearloose also sells red cerium batsticks which work well with darkside and battlaps.
Tom Mitchell