This little guy may not be regulation, but he sure does look sweet.
Note: this Instructable is for people who are familiar and comfortable with the lathe. Do not attempt this if you have never used the lathe before. And always wear eye protection and a dust mask when operating power tools.
You'll need a lathe, a power sander, a wood blank (I used walnut), sand paper, and a drill press.
Step 1: Wooden Blank
The overall length of the broken player I had was about 4.25" long. So I cut the blank to 6" long to give extra material on both ends.
I recommend using square stock that is pretty close to square, it makes the next step easier.
Step 2: Drill Holes
Note: If you are making one of these for a particular table, you should double check the measurements of your table's rods and mounting screws before you drill the holes. You want the player to have a tight fit on the rod.