We have 24 pounds of apaches tears that I collected in Nevada. We have been working at polishing them, but having lots of problems. The early tumbling stages went fine. My wife used a combo pack of polishing media that she bought on eBay. This is what we believe we used:
Course grit (70 Grit Aluminum Oxide)
Fine grit (220 Grit Aluminum Oxide)
Pre polish (500/600 Grit Silicon Carbide)
Polish (diatomaceous earth)

The polish was unlabelled, but we found out after the fact that the polish was diatomaceous earth.

Everything seemed to go fine up to the polish stage. The apache tears/obsidian came out looking worse than they went in. The diatomaceous earth worked awful on the apache tears/obsidan.

My wife put them back in for the pre-polish stage, and they came out looking better. So we tried to polish them again. This time we used cerium oxide. Again, the apache tears/obsidian came out looking worse than they went in. Not nearly as bad as what the diatomaceous earth did though.
Here is a picture of what the rocks looked like before (left) and after (right) the cerium oxide polish stage.
Apache tears/obsidian before and after polish.

So we are going to try again. We have read that we probably want to use some sort of filler to buffer the rocks and slow down the polishing. This time we are polishing them with cerium oxide & plastic beads.