Dennis, I had the hardest time finding pinfire cases. There were some 20 gauge primed hull on GunBroker for a awhile, but the are no longer there(and wrong gauge...). Though I might keep looking. I really didn't want to convert centerfire shells as I wanted a a true pinfire shell for the gun. The only place I found was expensive but high quality.
I order 24 and figure they would last me a lifetime. Here is the link:
http://www.hlebooks.com/pinfire/cal16-01.htm
And I attached a few pictures of when I first got them a few months ago. I haven't shot them yet and I really don't have a good excuse. The gun is a recent purchase and my first pinfire as well. I
will load these up this week and post a range report.
Good luck!