I'll assume you don't have access to a lathe.
Make or buy a center marker...
Veritas® Center Marker - Lee Valley Tools
Since both pieces have a rounded, cylindrical end, a redneck approach might work...
Obtain a funnel such that the workpiece sits about half-way down in the mouth. Find or make a pointed rod that's s good fit in the funnel spout.
With the funnel held level on the workpiece, insert the rod and tap it to make a center mark on the work.
Not terribly accurate but, hey, I did say "redneck".