  We consider a coupled nonlinear Schr\"{o}dinger equations describing an
atomic Bose-Einstein condensates coupled to a molecular condensates through the
stimulated Raman adiabatic passage loaded in an external potential. The
existence of dark state are investigated within the full parameter space
accounts for all the nonlinear collisions, together with the atom-molecule
conversion coupling and external potential. The results show that there are a
class of external potentials such as double-well, periodical and double
periodical, and harmonic potentials, where the exact dark solutions can be
formed. Our results may raise the possibility of relative experiments for dark
state in the coupled atomic-molecular Bose-Einstein condensates.
