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Any class that can cast cure at range if you take reach metamagic feat.
If your looking for a strong range class that can heal with out a lot of work. I recommend Hunter, Inquisitor, Witch, Oracle, Druid, or Cleric. In that order with the exception being hunter and inquisitor both do a really good job.
Hunters
Pros: Animal Companion to block for you.
Unique spell list that has gravity bow on it.
Con: Needs a animal companion to be fully effective.
No special ability to increase your to hit.
Inquisitor
Pros: Extra to hit and damage ability's.
Better over all self buffing spell list.
Con: Low number of feat's for any thing other then archery.
Archer paladin -- use shield other on your party members to take half their damage, then lay hands on yourself as a swift action, then smite with your archery.
Lifelink oracle would work too.
I would rethink your healing at range requirement a little bit. Hopefully you are planning on emergency healing, not spending most of your actions trying to heal, and being able to 'reach' whoever is in trouble easily makes sense. I think there are ways to do that without actual ranged healing though.
One would be acquiring a familiar. There are feats that can do this, and probably plenty of other methods as well. With share spells, you can have your familiar deliver the touch spell, effectively giving you range without a whole lot more investment. One great thing is that this would work with scrolls and similar things too, so your emergency condition removal can be handled pretty well as well. The big issue here of course is that most of the classes with ok healing are pretty feat starved to pursue this and archery. Witch though would be a pretty obvious choice, although low BAB makes archery problematic. In the other direction, a Ranger of Besmara can have a parrot familiar, which would be great archery but limited spell casting. A Druid can have the Eagle Domain, which grants a familiar, but other druid powers don't synergize well with archery. A grenadier alchemist with the tumor familiar discovery would also be a way to achieve this, but you would probably have to use wands (or scrolls with UMD) to get the charge, since recipients in trouble probably won't be able to spend actions to drink extracts.
Another way to achieve what you are trying is making sure you are very mobile yourself. If you can't heal at range, but can get wherever you need to be quickly, without spending actions, you achieve the desired effect. The obvious way here is being mounted. You can move around the battlefield while full attacking and then when things get messy you can cast and ride on in to save the day. You can even cast while riding in and then ride back out with a pretty easy concentration check, and if you need to use a scroll instead of a memorized spell you can pull if from your handy haversack with a move action you aren't using. While there would be some cases where it would be difficult to get to someone in trouble, or you might take AOO getting in, I suspect most of the time you will find that you can get where you need to be.
The big advantage of this last one is fairly minimal investment. Even a level-3 animal companion is usually sufficient for an archers mount, since you are avoiding most melee situations, so clerics, inquisitors and rangers can get this for free or just with a domain choice. Druids and Hunters of course have full power animal companions. Oracles can with the right revelation and of course there are feats out there for this too if nothing else will work.
Best class for this is a Divine Hunter Paladin. They have the ability to Lay on Hands from a distance and get all the ranged feats they need.
An inquisitor is nicely set up to do most of this, with a reach spell metamagic rod fairly cheap (3k i think)