Might as well put this here as no one else on any BL2 forums seems to have come up with an even remotely reliable legendary drop rate chart yet and it might help if I start so it can be refined and made a bit more accurate.
Ok, here's a list of every legendary Gun and their drop rate, based solely off my personal farming experience (and a couple of other posts I've seen on here in the past suggesting certain legendaries having higher drop rates that my farming seems to imitate).
Please be aware the following details may not be accurate. These are based on my own personal farming experience and could be highly off. Oh, and the stats I give here are correct. I farm a bit. Keeps me busy I guess.
Listed with highest chance first.
If the boss has a specific drop location and I have never got it from them I will state how many runs I've done instead and then declare NO DROP afterwards.
Given stats are based on a solo player on xbox with no mods used or exploits used (Master Gee / Hyperious area 4 way slider) unless specified. No Vault Hunter Relic used either if that makes a difference.
Maggie/Slagga - Mick Zaford/Jimbo Hodunk (1 Every ~15-20 Runs)
Longbow - Badass Creeper (1 Every ~20 Runs)
Norfleet - Vermivorous the Invincible (1 Every ~20 Vermivorous Kills )
Striker - Old Slappy (1 Every ~25 Runs)
Lyuda/White Death - Gettle (1 Every ~25 Runs)
Hellfire - Scorch (1 Every ~25 Runs)
KerBlaster - Midgemong (1 Every ~30 Runs)
Veruc - Mobley (1 Every ~30 Runs)
BadaBoom - King Mong (1 Every ~30 Runs)
Sledge's Shotgun - Smash Head (1 Every ~35 Runs)
Mongol - Dukino's Mum (1 Every ~35 Runs)
Pyrophobia - Incinerator Clayton (1 Every ~35 Runs)
Deliverance - Tumbaa (1 Every ~35 Tumbaa Kills )
Logan's Gun - Wilhelm (1 Every ~40 Runs)
Baby Maker - Mag Dog (1 Every ~40 Runs - Not sure what Mad Dog's/ Madame Von Bartlesby drops are now.)
Hornet - Knuckledragger (1 Every ~45 Runs)
Bunny - Chubby Enemies (1 Every ~45 Chubby Kills )
Gub - Laney White (1 Every ~55 Runs)
Bitch - BNK-3R (1 Every ~65 Runs)
Skullmasher - Son of Mothrakk (1 Every ~70 Runs - [FELL THROUGH THE FLOOR!])
Emperor - Hyperion Assassins (1 Every ~70 ALL 4 ASSASSIN'S Runs)
Flakker - The Warrior (1 Every ~75 Runs - [Look HARD!])
Volcano - The Warrior (1 Every ~75 Runs - [Look HARD!])
Gunerang - Rakkman (1 Every ~80 Runs)
Pitchfork - Terramorphous (1 Every ~100 Runs)
Unkempt Harold - Savage Lee (65 Runs - NO DROP )
Thunderball Fists - Captain Flynt (120 Runs - NO DROP )
Nukem - Black Queen (250 Runs - NO DROP [She spawned 68 times for me])
Invader - Saturn (250 Runs - NO DROP )
Hammer Buster - McNally (400 Runs - NO DROP )
Conference Call - The Warrior (450 Runs - NO DROP )
Infinity - Dr Mercy (800 Runs - NO DROP )
Shreddifier - Random Drop (Have got 10 drops from Hyperious in about 2000 Runs)
MadHous! - Unknown Drop (Was glitched when I was originally farming. Have got several through treasure room and Pete since.)
I'm aware that many of these will seem off to people, but as I said, this is just how my farming went, it's not very accurate at the moment.
I should also mention that if you can farm the invincible bosses quite easily, you should probably know that I've noticed this too:
Hyperious seems to have an increased chance to drop:
Norfleet
Shreddifier
Hornet
Sledge's Shotgun
Whisky Tango Foxtrot Shield
(I mean I've killed Hyperious about 3000 Times now and he's dropped at least 5 of each of these items so this is just speculation but maybe he has an increased chance to drop them)
Pete seems to have an increased chance to drop:
Vehicle Skins (only Runner/Bandit Technical)
Legendary Class Mods
Fast Ball Grenade Mod
Fire Bee Grenade Mod (almost makes it look like this is supposed to be his drop)
So there's the weapons at least. I can also post Shields/Grenade mods at a later date too if you wish (going to bed right now).
I hope it helps a bit at least!