I think you would find that, being an organic material, pearls will take a dye fairly well and easily. And once it is set the color will not rub off.

If you use Ritt or Tintext dyes, you should pull them out of the dye batch and drop them into a container of water with some vinegar in it. This will help set the dye.

Procion dyes would probably also work. You need to add salt and soda to get the reactions. Procion dyes have the reputation for being very permanent.