We always two healed it, though it wasn't easy before the debuff was as big as it is now. Specifically, resto shaman and holy paladin. Our raid comp had two people (mage and shadow priest) that could bounce an orb by themselves (we always did seven bounces) so the normal phase damage was much lower than it could have been. Given that you only have one person that can do a solo bounce, and the debuff, you probably should go with three.
You do have to dispel the disrupting shadows, especially with two healers. We split the healing/dispelling for normal phases essentially along the same lines as the black phases, but the healers need to know when they need to help out the other team, IE, I as the melee healer would have to heal/dispel the ranged group some if they got three disrupting shadows.
One thing to check is that your DK tank is using his tier bonus at the start of black phases. The damage starts very high and drops off as tentacles die, so having a cooldown for even just the first few seconds makes a big difference. The good part about the DK version is that it can be up for every black phase, the others can only be up for every other one because the phases are slightly less than two minutes apart.
As for healing the black phase damage, as a druid you can alternate tranq and tree form so you have a cooldown for every black phase. Beyond that, there isn't much to say other than basic druid stuff. Hopefully your raiders know how to utilize their own personal defensive cooldowns, as they should be using them at the start of black phases when they can.
Not really healing related directly, but your dps strategy for black phase should involve killing the weaker tentacles first, as the room wide damage is proportional to the number of living tentacles. This means the flails, then the eye, with the claw saved for last. Each of our two teams started on a flail, then moved onto a set of eyes. Specifically, from where the claw is, facing the center, our melee team started at the left flail, then killed eyes heading back to the center. Our ranged team started at the right flail, then killed eyes starting from the center to the far eye, then came back to finish off the claw if it was still around. Our combat rogue just stayed on Zon'ozz the whole time to abuse blade flurry to murder the claw.
Edited by Asthas on 5/2/2012 6:09 PM PDT