I would like to find local Darboux coordinates for symplectic structures on coadjoint orbits of some nilpotent Lie group. At first, I thought that this would be not very hard, and that it would be possible to find a change variables by simply playing with the Poisson bracket relations. But eventually I've got stuck.

So, is there a more or less general way to find Darboux coordinates on coadjoint orbits?