It is well known that bright parametrically driven, damped nonlinear Schrödinger solitons are prone to oscillatory instabilities which set in above a certain driving threshold. In this communication I shall demonstrate that the parametrically driven, damped dark solitons are immune from instabilities throughout their existence region. Furthermore, I shall show that for the undamped case there are two different stable solutions, which are also capable of forming stable complexes. I shall mention some noteworthy characteristics of the interaction of these different solutions.