I'm the happy owner of a Slovak made peening jig:
http://www.hvf.sk/naklepavac.htm Attached is an image with measurements.
The caps both have inside Ø=14mm, outside Ø=22mm. The profile of the edge on the first one is that from Ø=16.0mm to Ø=18.6mm it is flat, and slopes away to either side. The second one is flat from Ø=14mm to Ø=16.5mm, then slopes away.
The inside length of the cap is 36.5mm, outside it is 48.0mm long. I suspect the caps have been somehow hardened to resist deforming under hammer blows.
Hopefully the diagrams here make sense.
Everything is given as a diameter, though one of my blue markings looks like a radius, it is just meant to show where the diameter is being taken. The red diameter is (obviously) the diameter of the post to which the caps mate.
It is nice that a few things are less expensive in Europe-- my jig was 11€ and a Rozsutec stone was 2€-- things I keep hidden away because all of my neighbors have the idea that scythe stones are to be used not by firmly sweeping the flat edge against the blade, but by violently grinding down the scythe with the corner of the edge, leading to lots of oddly shaped old scythe stones lying around.
If you need any more details of the jig let me know. It looks like something pretty simple to make on a lathe.