They make an epoxy putty that works really well for this kind of thing and can be sanded and stained. comes in a plastic tube think the name is pc wood. works really well. leave the area rough and really press it in there after a couple hours or more carefully sand and finish. I have used this many times on different kinds of wood with great results. After you stain you can use a Fine paint brush to create any wood grain to blend with surrounding area.