The drawing should be self-explanatory.

One 3 1/2" length of 3/8" silver steel (drill rod) plus a 2" length of 2 " diameter mild steel. Make as per drawings.
Ensure that the punch is a nice sliding fit in the coned part. Either use a reamer to make the hole just over the size of the rod, or a 3/8" drill and turn the rod down to fit.
Make a nice sharp point on the end of the rod, then harden and temper.

I have made two sizes, the one shown, plus a smaller one, which has a maximum diameter of 1" and with a 1/4" punch.
Just scale the drawing to suit.