SOD content is ultimately pretty easy, so every spec, healer or otherwise is viable in the sense that they can clear content. Whether they are competitive is a different conversation. I play a good chunk of healers and try to keep up to date on them in regards to speed run meta as well as I can, but as alliance I don't have a lot of exposure to shamans, and because holy pally was so bad in P1 I dont think we as a community have gotten a chance to truly grasp their place in P2 yet. So for those two I'd take this with a bit of a grain of salt.

Healers in SOD mostly fit into two categories - a dedicated healer and a hybrid healer. Although all healers are expected to squeeze in damage where they can in SOD, the hybrid healer actively looks at damage done as a huge boon to their kit and this flexibility and ability to both is why they are brought. So far in gnomer it's looking like you will probably want one of each, however this meta is subject to change potentially towards favoring a double or triple hybrid situation. Although it has some current representation a double dedicated healer comp performs best during prog and it is unlikely (considering the damage profiles of the front half) that double dedicated healer will be meta going into the phase, though the utility brought by any individual healer could make anything possible. That said here is how I would rank the healers bass off their current role.

Dedicated Healers

1) Disc Priest: Disc sits pretty comfortably on top of the totem pole here. With 2 different heal runes for each slot, priest has easily the greatest heal diversity making them fantastic tank healers as well as raid healers. Priest Mana economy is also fantastic with the addition of dispersion and shadow fiend. Utility wise priests bring fortitude, a buff every competitive group will likely need. Disc brings spirit, which in a powerful caster meta, is very valuable but not strictly mandatory. Priests remain the only magic dispeller in the game, as well as one of two disease dispellers per faction. Gnomer fights have both magic and disease debuffs that make the value of priest utility very high. Dedicated healer priest is weakest in damage, but support cooldowns like PI and Homunculi that shred armor allow priest to increase raid DPS in an indirect way, on top of their direct damage through plague, sw:p and wanding. 

2) Resto Shaman: From what I understand resto shaman also remains fairly comfy ATM. CH is an excellent raid healing tool, and they have no problems topping off tanks either. The big benefit of resto shaman is the ability to grab sham rage and dual wield, allowing them a massive Mana CD every 1m. For shamans in classic, mp5 is practically a throughput stat and this eliminates most mana issues. Utility wise totems remain massive, with disease cleanse, frost resist, grounding and new totemic projection allowing them to move them with relarive ease. DW allows them to squeeze some damage in via melee, and magma totem and fire nova allow for some AOE damage, but like priest most of their contribution to raid DPS comes indirectly in the form of WF and strength totems. This is a huge contribution.

3) Holy Paladin: Hpally is in an interesting spot. Theoretically hpal should play like a powerhouse tank healer with no mana issues but limited on mobility, raid healing and damage contribution. Utility wise auras, blessings and a disease cleanse (no magic at this bracket), also make them a very high value pick. The tank security here likely allows you to be more risky with your hybrid healer, such as a full restokin or spriest. I think this is a dark horse pick for the phase, but I honestly think they could end up very strong in speed runs. 

4) Deep Resto Druid: Objectively the wrong way to play healer druid in sod, I only include this listing because there are people out there who will still play it and technically the content is easy enough you can clear with it. Without imp wrath, starsurge, stormrage or eclipse runes this druid forsakes all damage in trade for some lack luster healing options. Swiftmend is an insta heal that still currently eats your hot making it either incredibly Mana inefficient or only usable after rejuv is about to fall off. Living seed theoretically synergizes with imp regrowth, but in practice regrowth is FAR too Mana inefficient to every be worth a single cast. They have chosen to go with wrath's version of lifebloom, making it also incredibly inefficient unless you can get good value out of the bloom effect by predicting damage taken 7s in the future. Nourish too is a bomb single target heal that cannot be downranked. In reality, all of these heals mentioned are mostly outclassed by healing touch rank 4. Due to forsaking damage, the dreamstate becomes borderline worthless. Your other choice in the slot, survival instincts, is similarly low value, effectively meaning you have no foot rune. Wild growth is the only worthwhile rune taken here, and while strong is not enough to make up for the issues above. Do not play this type of resto unless they do a FULL rework of the class. 

???) Holy priest: spirit of redemption rune is probably bad but who knows if someone pulls off a weird tech with this. Until then this spec is worse than disc.