  The energies at geometries close to the equilibrium for the e$^+$BeO and
e$^+$LiF ground states were computed by means of diffusion Monte Carlo
simulations. These results allow us to predict the equilibrium geometries and
the vibrational frequencies for these exotic systems,and to discuss their
stability with respect to the various dissociation channels. Since the
adiabatic positron affinities were found to be smaller than the dissociation
energies for both complexes, we propose these two molecules as possible
candidates in the challenge to produce and detect stable positron-molecule
systems.
