If there is nothing wrong with the old gun other than some tape on the stock I wouldn't try to force him to change. It sounds like he is used to the gun and it probably holds a lot of memories for him and he wants to continue to use it. My grandfather used to hunt everything with his old Marlin 30-30 and even went elk hunting with it. Everybody told him he couldn't use it and had to get another gun to use but he refused. He ended up killing the biggest elk out of the group. I had a old .22 with the stock bolted back together that I used to hunt with until it got stolen and I liked it better than my new one. If the gun is safe to shoot I would leave him alone and let him enjoy his rifle. He sounds like he is not interested in having it replaced.