Immortal Rain - the female MC was raised by an assassin/bounty hunter. It's not part of the main story though. Instead, you may want to check out Touhou Shinigami: Meteor Methuselah Gaiden which is a side story for Immortal Rain that tells the story of said assassin. However, you'll only see the kid in the last chapter. Both are good stories, though, so I recommend trying them out. ^_^

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Can't believe no one mentioned The Breaker

Do you mean Hinamatsuri This mafia type guy raises a psychic girl who first blackmails him by sheer force then adopts him as a parent. It's pretty funny.

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Azumi definitely fits...

Dogs works, there's multiple stories but its the one with the girl.

TISTA raised by the church to be an assassin, but she had a father figure that tought her and was an assassin so I reckon it fits. One of my favs.

13 isn't really about the parenting but it has a girl who's parents are assassins.

Hunter x hunter has a family of assassins as a theme for one arc and a character back story...

Demon flowers- has kids raised by a demon assassin XD

Jormungand (seconded)

Owari no seraph raised?/kept prisoner by vampires.

Akuma no riddle? school full of wannabe assassins, it isn't the best though. Premise is pretty typical and the execution is slightly confusing.

Necro dancer they come from a family of demon slayers

Apocalypse no toride and Dendrobates also have child soldiers as back stories but they're only half a chapter of flashbacks worth at most.

Rose hip rose has a bunch of kids trained as assassins.

Number a kid that's part of an assassination organization.

Assassination classroom? alien teaching kids how to assassinate it in school, not raised by it though.

Nurarihyon no mago kid raised by yokai and is a quarter yokai.

Densetsu no Yuusha no densetsu and Akusaga also have it as back stories, but only referred to.

Monster and child raised by a vampire.

Amai kamiato also raised by a vamp.

Shirayukihime to 7-nin no Shuujin? maybe...raised by a particularly nasty military commander...

Innocent (SAKAMOTO Shinichi) family of executioners and how the young heir copes.

Vinland saga? raised by cut throat vikings, that raided towns and murdered most people in them, so mostly assassins? still kill people...

Dangu I'm not sure what they are...mercenaries maybe? all I remember is they kill people and raise the kid that way.

Do samurais count? If so Samurai chichi works.

Maybe nobody mentioned it because the protagonist wasn't "raised" by anybody but his parent(s?)... if you start counting martial arts teacher/disciple relationships, well, it becomes entirely something else. And you might as well move on into boxers and coaches, etc...

But... that doesn't really count! He's not "raising" him... much less is he an assassin or anything close. Murim doesn't really count. >.<

As for the others, will check them out one by one! Thanks! I do see a lot I already read / reading though.

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I only read the beginning but maybe Dogs: Bullets & Carnage