Is there a way to mount a crystal ball on a stair post finial?

I think trying to bore a hole up into the crystal ball will detract a whole lot from appearance of the ball. Drilling such hole would not be particularly easy and could lead to fracture of the glass if the proper tools were not used for the drilling operation.

If I were you I would make a visit to an old fashioned lamp store (the kind that sell all manner of lamp parts for building your own lamps) and see of you can find nice brass or chrome round lamp piece that was maybe 3 inches in diameter that you can re-purpose as a nest piece to secure the crystal ball. This piece can then be secured to your base plate board. I would use epoxy to secure the ball to the metal lamp part. Place the epoxy underneath so that it does not show.

I'd consider cutting a shallow hole in the top of the wood piece, such that the bottom of the ball hits the bottom of the hole while the sides of the hole contact the ball.

Then I'd use an epoxy to secure the ball in the hole.

I think you'd need some test pieces of wood and ball to try with, but if you made the hole not too small, then you'd have a good surface to epoxy to, and the ball should stay put.

i've actually done this myself and love the way it looks. can't tell you how many compliments i receive on it. but i think the compliments are because i took it a step further and ran some battery powered lights to them, so they double as night lights. i just glued them in place with an epoxy and they've been holding for 9 years and counting. i've included a photo of the ball and also tried to cover it up with a blanket to take one in the dark with the light on. the house is over 100 years old, so i don't mind it not being perfect. if anything, the glue looks like a bit of dust in there. i just noticed that the first photo also shows the one at the bottom of the stairs...

:)