I think you got a typo ...
There are 2 typos in the title and this one:
You can't drill a 2" hole in a 1" diameter end. You CAN drill a 1/2" hole in the end.
In a lathe, you can rotate the work, OR rotate the drill. Either way, a 2 ft long tapered piece will be hard to drill on center. If you are making these tapered pieces, drill the holes first before you taper them. If you can, make a short round shaft on the end to hold your steady rest support, them drill them using the tailstock and a 1/2" drill bit. Are you using a metal lathe? How long is the bed?
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)
Last edited by woodnthings; 11-10-2018 at 11:21 PM.