We present accurate ground-state energies for the positronium atom in a Coulomb field of point charge Z (XZPs), for the positronium hydrogen (HPs) and positronium lithium (LiPs) atoms. Calculations are done using the diffusion quantum Monte Carlo (DQMC) method. For XZPs, the critical value of Z for binding is examined. While HPs is stable, the results show that LiPs is unstable against dissociation to a lithium atom and a positronium.Peer reviewe