"Cheap cue lathe, complete" is a bit of an oxymoron. Complete- nothing's cheap.
To "taper shafts only" does not warrant a complete cue lathe. That Bludworth CNC TS machine that was listed on here a few days ago would taper shafts/butts.
But then, how to put on ferrules, tips, shaft inserts and collars? There's the rub- you need a complete cue lathe (or full-sized lathe complete w/taper bar.)
If both what Rick and I have offered is not to your liking, perhaps you've narrowed down your search and should post your price range, etc.
To some, buying a machine for half price is cheap. For others, that's still 3x more than the price they have in mind.
Best of luck.