Im not too familiar with the good properties of parsley but I've heard it can be high in calcium which isnt a very good thing for bunnys. So just dont give lots of it.
Might as well stick with Cilantro
When my turdlets were little I would go through 2 large bunches of Cilantro per week, I would imagine at 4lbs each now, 3 bunches/week sounds about right... if that helps you at all for ammount fed. This was ofcoarse with a whole whack of other leafy greens.