Framing for drywall around curved stairs
I would install thin, flexible boards against the wall and mount crossbars (ceiling joists) to them. I would not mount drywall directly to the stairs.


Establish lines on the wall. This could be done with semi-rigid pipe held against the staircase to create smooth curves. 
Rip 1x4 boards in half to yield 1x2 boards with nice square edges. 1x2 lumber usually has very rounded edges.
Mount these runners on the line with the narrow edge and square corners against the wall. Use 3" construction screws and pre-drill so as to not crack the boards. If you find the curves too tight, soak the boards in warm water for a few hours.
Mount 2x4 boards flatwise across the span, screwing them into the runners with 2-1/2" construction screws. Pre-drill here, too. 


This strategy, along with the corner tape joints, will leave you with a very strong ceiling. It'll be isolated from the staircase, so that any vibration and movement in the stairs won't result in cracks. 

| &lt;-- wall
|__________
|          | &lt;-- 1x2 runner, screwed to the wall studs
|__________|_________________________________________________________
|
|     2x4 ceiling joist, screwed into the 1x2 runner
|
|_____________________________________________________________________ 
|


One suggestion for fitting the drywall (the most challenging part of all this) is to do it one side at a time. Fit pieces that run about 2/3 the way across the span to the wall. Do this from each side, mounting loosely near the walls and lapping the center area. Then use a rotary cutter to slice up the middle through both layers. Remove the scrap and screw it all tight.