Allan, I assume that you are talking about real goatskin. You can buy this at Tandy Leather. I would guess that you should be able to glue, sew or rout out a section and replace that with the new goatskin. This is difficult to say without looking at it--and I have no experience with this direct problem--but I would guess that you could come up with some reasonable fix with the products that you can get from Tandy.
If you have a leathercraft store in your area, try them and ask if they have a customer that might be able top help. Another potential is an oldtime shoe repair store.