I have found that cyanoacrylate glues are wonderful for this application.
They are available in colors, including black.
They are available in different viscosities from water thin to gel.
When cured, it can be shaped, sanded and polished.
Look up a company called Glu-Boost.
Their products are specifically designed for musical instrument repair and finish matching. You can fill chips, wick into cracks, and color match existing finishes.