Tedious we know but first determine specie of wood. Rosewood was very common to many of these. I soak the veneer in a glycerine and water solution for perhaps one day. Then I wrap it around a piece of wooden dowel or brass stock close to the radius of the damage. Let it dry for several days, remove from dowel, and apply. If area is large - replace it entirely. Patching small areas is of course the most challenging if you're trying to match existing veneer. G'luck matey.