One good thing about starting with a sphere for an eyeball is that the points are positioned to make a great 'base-beginning'.
If you drag out a sphere and look at the top, you can see the points you could manipuilate to make the pupil or iris 'move'. (morph)
If you start with a spherical shaped eyeball, Rotate so the top is the front, then adjust the outside shape to fit the 'odd-shaped' eye socket.
Then add the morph targets.
You could then morph/(move) the pupil and iris , and not actually need to 'rotate' the eyeball itself.
The only bone you might need could be a fixed bone in the head, if you wanted to add the eyeball to the figure seperately, in figure mode.
The tut that Jehovahenker posted a link to concerns rotating a whole spherical eyeball.
I nearly finished part 2 last night, but not quite'
Its a cartooney eyeball as well. pretty straight forward.