It seems everyone else is focusing on a melee duo team, and following that, I'd propose RDM/PLD + DRG/BLU: it's freakin' sick. DRG/BLU gives good damage output, ridiculous healing capacity (basically bottomless healing as long as they're refreshed). RDM/PLD gives good damage mitigation/hate control, decent damage output, and a slew of enfeebles to cripple any monster, not to mention emergency cures, Refresh for your DRG, a mini-Invincible* every 5 minutes (obviously when used with Convert, you can get a safe vert-under-fire while also getting some nice spike hate from double enmity Cure IVs), and a JA stun.
Not to mention Death Blossom > Drakesbane = Light.
*As in, the mob would need to be hitting you for (Phalanx DR + 1) * 10 damage (250 damage with a 24 DR Phalanx) normally to damage you at all at the beginning of Sentinel. A normally 500 damage attack would deal 26 DMG, etc. The effect does get weaker over time, but is easily enough to make your SS last through your Convert + Cures.
A very situational setup^^
I can't speak for everyone, but I like to low man as much as possible. This includes all situations, not just special circumstances. The main problem with DRG/mage soloing is their total reliance on their wyvern pet to heal them. Long time ago back when I first began playing FFXI, I noticed a disturbing trend. DRG's are not very AoE friendly one bit. All it takes is a few bomb tosses or another form of nasty Aoe and say goodbye to your wyvern for 20min. I might add that most attacks that go though shadows often wreck havoc on a wyvern. Our DRG in our Nyzul static really hates Flayers, frogs, and those damn chariots.
Frankly our best duo partner is another RDM. You might take longer to kill sometimes, however it's the safest best for success across the board. In a non-situational duo, other jobs can do ok. THF is a good tank if they are smart enough to steal your hate. NIN/dnc can solo almost anything by themselves so a RDM partner just helps them along. There is no ideal partner for all situations, you just have to adapt and hope it works.
If it doesn't happen, we're left with just one option. While we can talk about PlayStation 4 as a mid-range PC in a miniature box, to comprehensively best the console's most powerful elements, once again it seems likely that PC owners will need more money to brute-force their way through to improved performance. Source