We investigate possibilities of existence of inhomogeneous dark states of atomic-molecular Bose-Einstein condensates loaded in trap potentials. The system is described by three-coupled equations of the Gross-Pitaevskii type, which account for contributions of the kinetic energy, two-body interactions, and an external potential, and which govern the conversion between atoms and molecules in the stimulated Raman adiabatic passage. We report a class of trapping potentials allowing for the existence of localized stable dark states. The respective atomic and molecular distributions are computed, and their stability and dynamics are discussed.