Flaring the conical end of a metal ring

[DLANDINO]

I have a question about metal working and I was wondering if you have any idea of a tool or tools that can be used to flare out the tapered end of a metal ring. I started making rings out of silver US and foreign coins as a hobby and it seems that people love them. So when I poke a hole in the ring and bang it down a mandrel the ring ends up being conical in shape until you flare out the narrow end. I have been using a dapping block to do this but can damage the ring if not done right. I was searching for a hand operated tool that can widen the narrow part. This is an example of the work I have been doing so you can see what I am talking about.