I'm pretty well geared at the moment, but let me try and give some tips.
Firstly, how many healers do you use. I presume 3? Do you have a dedicated tank healer(pref a pally)?
1 healer in group 1 and 1 on group 2. Group one is on one side, second on the other, close together so you can share some CoHs and PoH. Although I never use CoH or PoH, unless in feud phase.
When a person in my group gets to 1 hp - I only use Flash Heals. Heals are too slow. Way to slow. The chakra is for Serenity, helps a lot. If a member of my group and myself get to 1 hp I use binding heal. Does wonders.

Flash heals are quite mana intensive, but the fight itself is not that hard for healing. Hardest parts should be feuds, where you stack up and try keep everyone up. We heal this usually with 2 priests and a pally. Flash heals are best to keep your person above the 10k treshold. Do NOT use CoH as a quick way to save a person. Unless it critts you will not heal ur person fast enough and then you'll be forced to use a Flash heal, because any other will be too slow. My tip would be to use only Flash Heals to keep your people up the 10k mark and the rest of the time slack and gain mana and help on tanks.

Once feud starts. Sanctuary might be a bit too mana expensive if you're not very good geared. If you feel comfortable, prepare it before the feud starts and pop it benath the raiders. Immidiately spam those PoHs, CoH and PoM. Ig you have a shaman or a druid, let him spare a healing cooldown. Usually let them help in second or third feuds, when your mana is at it's lowest point.

So to recap.
1. Flash Heals are fast to keep 2 people in your group above the 10k. Do NOT use Heal, CoH - be sure he is up!
I'm not renew specced, so I almost never use it. Maybe sometimes on the tanks and when I have mana to waste...which is pretty often as of late.
2. In feud phases - if you feel comfortable pop a Sanctuary. Spam those PoHs and CoH on cd and keep the PoM going. If you feel that the healing is lacking, forget the PoM. It's global cooldown can cost you a raider. Keep spamming PoHs. If you see a person at critical hp - Flash Heal immidiately.
3. Do not overheal on slime phases. People just need to be over 10k and that is easy. The fight itself is hectic for healers, but that is due to the fact we are used to seeing people topped of. And every time we see someone drop to 1 hp we freak out.

Stay calm, use those imba fast Flash Heals and you'll do it.
Good luck.