This may seem obvious, but you'd be surprised: Someone who knows how to play their class and didn't roll it up as a FOTM. After that, it's having spells/CAs leveled up and geared appropriately.
If too many mobs are pulled, no healer (or even pair of healers) can keep people alive due to guk strong reducing all incoming heals.
As others have said, i believe most healers (if properly geared) can be successful in challenge. My fury is in T1 heroic (other than BP), still missing a few infusers, and was able to solo heal challenge Sambata a few times by saving Cheetah and such for the right times.
I solo healed the first couple of bosses in Challenge Sambata on my Defiler. Gunk the Trunk..though...haven't quite gotten him down solo. Have duo'd him with one of our wardens though.
1- Make sure you have an actual tank that is built to take heroics 2- make sure you DPS are well played, leeroy Jenkins need not apply. 3- With that I solo heal on my channeler. 300m hp, 155k pot, and still pull 1-1.5 billion dps. However, it is much more fun and relaxing to just bring another healer. Inquis with a melee group makes it much more fun. If we have an inquis lfg, im'a take him with us for sure.
It really depends on the player. My fury has solo healed all but the new Diaku zone. A lot depends on your gear, your spec, and timing your spells (such as damage reductions).