I would use superglue and sawdust for a filler, put in a couple drops of superglue, sprinkle in some sawdust to fil the hole, soak the sawdust with superglue add more sawdust to make a mound and pack the mixture in with a popsicle stick to where it is packed in tight and above the hole. Let the patch cure for and hour or so and file or sand it back down to the normal contour.
I just filled this hole yesterday, I had some rotten wood on the side of an osage billet I spliced up. I thought I would be out of it as I shaped the handle but it was still there, I made a super glue sawdust patch to fill the area. I use the same stuff to fill a variety of voids I encounter in my bow building.
Not bow related but on my latest flintlock build I really slopped up the nose cap fit, I rebuilt the lost wood with superglue and sawdust and started over. My patch is probably 10 times stronger than the original wood.