If we're just throwing out ideas then a Halfling Reliquarian Occultist using a Shadowshooting Double Crossbow would deal respectable damage while also having a lot of utility.
Spellcasting, skill ranks, and a lot of mental focus.
If you want something that would really be a force multiplier for this melee-heavy group then I'd recommend a feinting Dwarf or Drow Inquisitor to spam out AoOs through Improved Feint Partner.
With so much melee, a skald is really tempting. The skald could also handle a lot of skills and the face role if no one is doing that already.
if you'd like to range + buff and such the arrowsong minstrel bard can ,from 2nd level, shoot at enemies in melee with his buddies without them giving cover (and he get free precise shot). you can drop a haste or something if you fight the BBEG and the party need even more boost then just your inspire song. and range while they do the close fight. it work very well with a bunch of melee party members.
(keep a glitterdust for invisible enemies, a grease to help against grapplers and your golden).
also there is this nice bow-string to help keep your performance running all day (or close to it. it also make your bow your sting instrument so that saves you hands)
When all else fails, pick up ye old HornBow...
Shaman's Apprentice Half-Orc with Sacred Tattoos and Fate's Favored... +2 luck bonus to all saves, darkvision, Endurance, and access to the aforementioned Orc HornBow.
Arsenal Chaplain Warpriest if you want to deal all the damages, but Arcane Duelist Bard [archer] or Arrowsong Minstrel Bard or Eldritch Archer Magus would add some arcane magics to the mix. There's some pretty gnarly Inquisitor archer builds, too. Nature Fang Druid ain't bad, but doesn't offer you anything that makes it any better than the others.
Depending on the campaign, a fourth melee might lead to chocking up in narrow passages.
In general, I agree with Sysryke that there's a million things that could fit here. There aren't any gaping holes in the party. Some arcane or psychic casting could be nice, but isn't mandatory or anything.
it appears that your group in lacking in the buffing/and healing departments as well (depending on your Oracles build choices).
Nah, the Alchemist covers that better than a Bard could (presuming they take Infusion, which basically everyone does).
I mean, I think Bard would be a good fit, but not because of healing.
With so much melee, a skald is really tempting.
Skald and Barbarian don't really mix well, sadly.
Investigator or Bard would do nicely as a Party Face/Skill Monkey.
Sorcerer, Archmage, Witch, Shaman, Wizard, or Druid would fit nicely in that group too-- playing a 9th level caster in a group that has that much melee is cruise control for awesome.
On the healing side of things the two classes would seem about comparable, though I'd think the Bard being spontaneous gives a slight edge.
Bards are lacking a couple condition removals that Alchemist has, and since an Alchemist can leave extract "slots" open, and prepare an extract in a mere minute, it is really good at removing conditions outside of combat. That said, Bard is actually much better (and probably the best in the game) for infight removal (i.e. removing volatile conditions), with Purging Finale, Reinvigorating Wind, and Song of Kyonin, so those two complement each other fairly well. But it's not something the party is explicitly lacking, in my opinion.
On the buffing side of things though, wouldn't the Bard's performance and access to group buffing spells be more efficient than the alchemist doing one person/buff at a time?
Ah, I only intended to respond to the healing stuff. Sorry!
The rage song gives the barbarian a chance to rage for more rounds throughout the adventuring day (choosing either to accept the song boost or use their own rage), and many of the rage powers are still accessible whilst in any rage.
In most campaign, the de facto additional rage rounds don't do anything past a couple levels, as the Barb never runs out, anyway. In either case, the bonuses (and rage powers) don't ever stack, and thus in tough fights, the Barb doesn't profit form the Skald's song at all. From personal experience I can tell you that's not satisfying for the player, when everyone else gets better when the Skald starts to sing, and you don't.