Use wood. Make a thin wedge-shaped piece from the same kind of wood as the piece with your crack in it, use a saw to widen out the crack a bit and give you smooth sides, then apply some wood glue and tightly fit the new piece into the crack. Leave it standing proud until the glue dries, then plane or sand it flush. Use care to match the grain direction and color of the top of your wedge to the repair site. You can make an essentially invisible repair that will stain perfectly.