Pokemon with the Crush specialty are the shortcut for Black Paint. Manual gathering works too, but a dedicated helper means you're never caught short. It goes into 3 recipes, so having a passive supply helps.

Paint used to color items black

Raw Material
SpecialtyRandom Bonus from Crush Processing
Crush specialty
ShopSmearguru / Palette Town Shop
Bleak Beach (Smearguru hut), Palette Town (Level 5)
MagmortarCrushBastiodonCrushShieldonCrushDugtrioCrushAurorusCrushPupitarCrushRampardosCrushAmauraCrush

You can craft Paint Balloon Beige, Paint Balloon Black and 1 more using Black Paint. These 3 recipes are mostly Other items that help fill out your island.

3 recipes
Paint Balloon BeigeOther
White Paintx1›Black Paintx1
Paint Balloon BlackOther
Black Paintx2
Paint Balloon NavyOther
Blue Paintx1›Black Paintx1