Let me start by saying I have never done that. But if I were to try it I would use a piece of thick scrap cloth, maybe an old pair of jeans something close to the thickness of your hide, and cut out a rough shape. Then I would use clips to hold the material on the quiver at the same spot and on the back side start marking and cutting until there was a fit I could live with. That would give you a good pattern to use.
If you are real careful you could use Barge cement to apply it to the quiver or a small drill bit to make a hole in both and stitch the bottom. There was a build-a-long on here a few weeks ago where a fellow showed a couple pics of his stitching when he added leather to a quiver.