Turn at a reasonably slow speed using a Forstner Bit. You will have to constantly work the bit in and out. The piece should be turning and the Forstner in the drill chuck mounted in the tailstock. Go in about an inch or two deep and then change to a regular drill bit using the same techique.
I am assuming you have the proper chucks.
The other method would be to drill the holes about 1 inch deep on both ends of an oversized square blank about 12" long. Glue a dowel into each hole and let dry.Then cut the end going onto the tailstock flush with the blank and mount the other end into the headstock chuck that will be spinning and turn the piece as you normally would. When the piece is turned to your desired shape just cut both ends off. Depending on your chucking ability, you can make various adaptations of the above.
Tony B Retired woodworker, among other things.
"Strive for excellence and settle for completion" Tony B