So, lets start this post out by recognizing three things:
1) There are at most a handful of fights in the game right now that would suit a BRD/NIN tank.
2) This would be competitive with level 75 era "holding" tanks like NIN/DRK and RDM/NIN, not with level 99 "tanks" that are basically DDs with some form of substantial damage mitigation/negation.
3) I'm mostly making this post to collect feedback from others before I try to do it. I think it could be fun to tank things on bard and my LS has two excellent bards (but not many people total).
Advantages:
Horde Lullaby/Foe Lullaby/Foe Lullaby II - 240 CE, 24 second recast
Horde Lullaby II - 320 CE (for some reason), 24 second recast
Any Threnody, Elegy, etc. - 240 VE, 100 CE
I haven't actually tested the VE values of Lullabies, because it would require me to find a low level monster that resists my lullabies (like Light Elementals in Qufim, which means waiting for an Aurora).
Now, you might look at the above and be all "okay, wat? How will that let me tank?" Well, Bard can get 80% Casting time reduction with a good build, making these songs almost instant. Also, using a set like this should effectively eliminate their recast:
Assuming 2 seconds per song, Bard could cap Enmity with the above build in approximately a minute. This is, you'll note, not even considering Nightingale, which could be used to let the bards cast even faster.
An aside on damage mitigation:
Sentinel's Scherzo and Earthen Armor with BRD/NIN HP pretty much take care of TP moves and spells (95% damage reduction for TP moves that would take >75% of your max HP), but you could also do the 50% PDT/MDT route if you didn't have Earthen Armor or for "oh ***" moments. Utsusemi recast is a non-issue.
Competition:
Currently the only tanks in the game are Paladins with Aegis and Ochain. For events where shield blocking is useful (like holding a bunch of monsters in Voidwatch), Paladin will still be the clearly superior option because they don't actually need to cap hate and their durability advantages against autoattacks will win the day. However, the game's recent lowman shift has led me to look for lower-man alternatives. If we need to do a fight (like Arch-Omega) with PLD, WHM, and BRD already, what if we could have the BRD tank and switch the PLD to RNG or SMN? Excalibur is less impressive than it was at 75. Many monsters currently resist Atonement. It's perfectly reasonable to think that a RNG could outdamage a Paladin against many new monsters.
Strategically, Paladin's weakness is still their lack of any way to generate substantial CE other than their sword or MP inefficient cure-force sets. Take Arch-Omega as an example again. He starts out in Four-Legged mode (physically resistant), which means that any successful magic DD (except Summoner) is going to rip hate off a PLD quickly by capping VE and CE. BRD/NIN doesn't have this problem. Flying Wyrms. Kited fights. Doesn't matter. Spam Spam Spam.
Anyway, that's all I've got. The promise of new wyrms with Seekers is bringing my attention back to Paladin's weaknesses.