I personally always use muriatic acid to clean rocks (except for calcite of course), including river rocks, and then give them a good soak in baking soda water for a full day to extract the yellow. It's really toxic stuff though -  you need to be REALLY careful with it (especially when it's pure), to not breathe it or get it on your skin. That as far as I am concerned that is the best stuff I've used. Iron Out hasn't worked well for me... Maybe oxalic acid would work also though, I hear it does but you have to heat the water slightly from what I've read. If you don't want want to go that hardcore, try vinegar. But you know petrified wood is pretty hard so I am not too sure about how much cleaning it will do.

If you go with muriatic acid (which I swear by esp for rusty orange stains), make sure to again be really careful and don't let the water get near any metal because it will destroy it, and also don't pour the acid down the drain - deposit it, diluted, outside, far from any kind of running water or plant life or whatever.
I'll wait for others to chime in.
Do you have a pic of the petrified wood ??? 

Thank you for the advice.  My boys and I have found some cool pieces along the Neuse River in Goldsboro.  These pieces were mainly found on 2 separate hunting trips.  The black piece has pyrite crystals on it.  I just noted this morning that the black is starting to deteriorate.  I suppose it is not 100% petrified, but the crystals are beautiful.

Good luck with the cleaning, BP.
The black wood is actually called "Lignite".
Here's a link so you can read more about it,
https://en.wikipedia.org/wiki/Lignite