This is the system I use (Davide Sora) to dye pearwood strips black. It is an ancient method, traditionally used by luthiers:
1) For a liter of water add 6 g of potassium hydroxide (KOH) (formerly called potash). Boil the pearwood shavings (still rolled up but not too tightly) in this solution for at least an hour, after which rinse them thoroughly in running water.
2) For a liter of water add 20 g of Logwood chips. Boil the pearwood shavings in this solution for at least an hour and leave them to soak for 24 hours. Then rinse them thoroughly before moving on to the next step.
3) For a liter of water add 12 g of iron sulfate (FeSO4) (formerly called green vitriol). Boil the pearwood shavings in this solution for at least an hour and leave them to soak for 24 hours.
4) Finally, rinse the shavings thoroughly and let them dry. Before complete drying, spread the strips between two flat wooden boards, interposing strips of paper to keep them separate. Allow them to dry completely between the two wooden boards and the paper strips for several days, checking from time to time that molds caused by humidity do not develop, eventually replacing the damp paper strips with dry ones.