I can think of three ways to do it off the top of my head, although I have no idea if any of them would actually work.
1. Make the punch as I did above, but drill an additional smaller hole at the bottom of and centered on the main hole. Insert a small pin to act as the punch for the pupil. (Maybe braze it in place? If you did, you probably wouldn't be able to do a proper heat-treat on the punch.)
2. In a piece of high-carbon steel, forge the eye you want with a normal eye punch and dot the pupil with a center punch, Harden, and hammer the end of a heated rod into the eye to form it to that shape, like some people do to make their touchmarks.
3. Drill the hole in the end of the punch blank with a hollow-center drill bit. I don’t know where one might get such a thing, but presumably a machinist could make one.
This is all purely theoretical, and as I said, I have no idea if any of these methods would actually work. Might be fun to try, though.