You can choose special inks to engrave the wood and stain it with a color that can be rubbed off.
Acrylic paints are widely used for wood engraving and have good adhesion. You can choose water-based acrylic paints, which can be easily washed off with water, or oil-based acrylic paints, which require special solvents for removal.
Alcohol-based markers can also be a good option for coloring wood engraving. They have good adhesion and can be easily removed with alcohol solvent or isopropyl alcohol.
As an alternative to paints, you can also consider using wax or oil to paint over your wood engraving. These can be applied to the surface and then washed off or removed as needed.