In the College of Winterhold's living quarters, you can find a black market merchant named Enthir - he'll sell you Black Soul Gems for something like 1200 or 1300 septims.
gaming.stackexchange.com/users/7816/Ian Pugsley
You can also find them in Geode Clusters in Blackreach.
It isn't a merchant, but it is mineable.
Note that you'll also get other things:
corundum, normal soul gems, and occasionally gems.
gaming.stackexchange.com/users/10650/thegrinner
Your best chance is to find necromancers and taking it off of their corpses.
I don't think there are any stores that sells them.
gaming.stackexchange.com/users/3917/l I
I've also found several Black Soul Gems off of Giants.
But unless you're able to snipe them then that can be a hassle.
I also heard somewhere that the dungeons rest every 40 game days or something like that.
(Not exactly sure, and haven't really been paying attention to the date in the game)
If so then Illinata's Deep, the old ruin thing by the Lady Stone would be an excellent place to collect them.
When I went through it for the quest, I found at least 3 since it's crawling with Necromancers.
I also find them off of vampires usually, but be sure to bring lots of Cure Disease potions if you don't want to turn into one.
gaming.stackexchange.com/users/15724/StardustLuna
Go to the college of winterhold and speak to enthir.
He will have two deadra hearts and one black soul gem.
After you buy what you want you need to save and then kill or hurt him.
After you do that you need to load that save
and he will then have two more deadra hearts and another black soul gem.
Repeat this process as many times as you want.
gaming.stackexchange.com/users/21513/skyrim master
Buy one from Enthir in the hall of Attainment, wait two days, and repeat process.
Also, you can find them on any type of HOSTILE mages, in warlock dungeons, vampire caves, Thalmor Justiciar groups might have them, and hagraven nests.
gaming.stackexchange.com/users/51160/Tommy Crane
Go to the college of winterhold.
Once you enter the courtyard there is a door on your left called "Hall of Attainment" go inside.
Travel directly across the room to the stairwell and go up the stairs to the next level.
Once you on the next floor go into the first room on the left.
This is Enthir's room.
He sells and buys stolen goods.
He has an empty black soul gem.
Once you have purchased it you can exit out to the courtyard, then wait 48 hrs
and you can go up to his room again and he will have another one that you can buy.
Just repeat the process until you have as many as you need.
Also remember to bring a pickaxe with you when you go on the mission in BlackReach.
In there you have a lot of mining to do and you will get a ton of soul gems of every kind.
gaming.stackexchange.com/users/54897/Ashley
You Find Black Soul Gems in College of Winterhold, but mostly random in dungeons, they're more common as you level, but they're still more "rare" than most regular Soul Gems
gaming.stackexchange.com/users/16733/Joe Ryan
There is one selling at Morthal, if I'm not mistaken Falion is his name, he's in the house nearest to the dock.
gaming.stackexchange.com/users/21955/haha
So far the best place I've found is the guy in The Colledge of Winterhold, but you have to join the Thieve Guild (I think) first.
Other then that, as you lvl up, you'll start finding them more and more through raiding the dougens (forgive the spelling please)
But I'm' still trying to figure it out how to acquire a lot of them, I remember back in Oblivion, there was a a casket or whatever you would place Grand Soul gems and after one night pass, they'll turn black.
But just keep raiding doungens and lairs, you'll come across them.
Also, htere's a quest, Azura's Shrine, two ways to complete that, one way: be the rightguess player and have it turn tnto a reuseable Grand Soul Gem, or be like me and keep it a Black reusable Soul Gem.
I think you have to be a level 5(five) to get this quest and that's by asking about rumors in the Inns or pubs.
gaming.stackexchange.com/users/34141/Cadeus
I've missed the chance to get the artifact that acts as a permanent black soul gem so I'm looking for them elsewhere.  Which merchants regularly sells black soul gems I can use?
Where can I find black soul gems?
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gaming.stackexchange.com/questions/36890
gaming.stackexchange.com/users/3015/Rapida
You can can find them in Blackreach, Giants or in the College of Winterhold's living quarters. A black soul gem could be found in certain locations or by specific NPCs.
A black soul gem could be found in certain locations or by specific NPCs.