The only way to farm Black Magic Spheres in Final Fantasy X is by bribing Black Elementals. 200,000 gil gets you two spheres.
And Black Elementals are only found in the Omega Ruins. So head there with plenty of gil if you plan to farm these things.
Note: you can get some Black Magic Spheres from drops as well, but only from one-off boss fights. These are the boss fights that can drop Black Magic Spheres: Seymour, Evrae, Evrae Altana.
Since these bosses are not repeatable, these aren’t an option for farming.
Uses For Black Magic Spheres
Black Magic Spheres allow a character to instantly activate any Black Magic node on the Sphere Grid that has already been activated by another character.
For example, if Lulu has already learned Flare, then Yuna can use a Black Magic sphere to learn it instantly without having to move onto that area in the grid.
Magic +10% can also be customized onto weapons using Black Magic Spheres. And you only need x1 Black Magic Sphere to customize this Auto-Ability each time.
Also, like with most items in FFX, Rikku can utilize Black Magic Spheres in her Mixes. Here’s a few worth noting:
FreedomX (Three Stars + Black Magic Sphere): Reduces MP cost for Abilities to 0 for the whole party.
Hot Spur (Elixir + Black Magic Sphere): Doubles Overdrive gain for one party member.
Brimstone (Bomb Core + Black Magic Sphere): Deals damage to all enemies and inflicts Poison, Darkness, Silence, and Sleep.
Are Black Magic Spheres Worth Farming?
Yes and no.
If you’re just entering the endgame, then it might be worth your time and money farming in the entrance to the Omega Ruins to help bolster your casters a little bit before moving on.
However, gaining AP isn’t too hard. And you’ll be rolling in AP as you explore the Ruins anyway.
So getting each party member to move over to specific spells that you want to learn won’t be too hard.
In summation: Black Magic Spheres are useful as a means to an end, but not much beyond that.
Even the Magic +10% weapon auto-ability can be made (or found via drops) through easier means.