I'll stick my neck out and say that perhaps you are selling yourself short here. The cool thing about a sphere is that the "center" can be anywhere on the surface

So, take a hand file, any flat hand file, and file a small flat anywhere on the ball (yes, that's the "center"). Then put the ball in a vice with the flat part up. If you can line up a pool shot, you can line up the ball with sufficient accuracy. Take a hand drill and a 3/16 bit and drill straight down an inch or so (through the flat part, good luck starting a drill on the spherical surface), that's all the hole you need. Now grab a 1/4-20 tap and tap holder (OK, if you don't have these grab $10 and run down to the hardward store and buy them) and tap the hole (you'll only get threads in the top 1/2" or so, but that's OK too). Repeat with the other ball. Cut a piece of 1/4-20 rod about 1" long and clean up the cut threads (with a triangular file), coat in fresh epoxy, and thread into a ball ... again repeat with other ball, then grab a beer 'cause you're done !
Dave, not really sure that 3/16 is the correct drill for tapping 1/4-20, so it would be wise to check this bit of Internet related information/folly