I have a Diamond ball polisher. I use one of the two products recommended by Diamond for use with their machine - Maguiars Ultimate Quik Detailer.
They also recommend the Aramith ball polish but I prefer the Maguiars because it isn't so pasty/creamy but more of a liquid that works from a spray bottle so it doesn't gum up the pads and is easier to use. I just set the balls in motion and give them a couple of squirts while they're spinning. It also isn't gritty so it should cause less wear over the long run.
I used to use Brillianize when I did them by hand. When I got the Diamond I tried both the Brillianize and the Maguiars. The Maguiars polished the balls better. Neither of these products leave a residue.
Give the Maguiars a try, it's only about $10 for a good size bottle. If you end up going with something else you can always use it on your car. They have a couple of different "Quick Detailer" products and an Ultimate Quik Wax that's in a very similar bottle, but specifically get the "ULTIMATE Quik DETAILER" as recommended by Diamond:
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It's available at most big box auto supply stores.
I've tried most of the cleaners and I find this product to be an excellent choice. It's also easy to apply while the cleaner is in motion. Thanks for turning me on to it.