Direct conversion between thermal and electrical energy can be achieved by thermoelectric materials, which provide a viable route for power generation and solid state refrigeration. Here, we use a combination of energetic, electronic, and vibrational first-principles based results to predict the figure of merit performance in hole doped single crystals of SnS and (Pb,Sn)S. We find high ZT values for both materials, specifically for (Pb,Sn)S along the b-axis. Both SnS and (Pb,Sn)S have excellent power factors when doped, due to a combination of increased electrical conductivity (due to doping) and a significantly enhanced Seebeck coefficient obtained by a doping-induced multiband effect. Anharmonic phonon calculations combined with a Debye-Calloway model show that the lattice thermal conductivity of both compounds is low, due to intrinsic anharmonicity, and is lowered further by the random, solid solution nature of the cation sublattice of (Pb,Sn)S. (Pb,Sn)S exhibits a high ZT plateau ranging from 1.3 at 300 K to 1.9 at 800 K. The overall ZT of the hole doped (Pb,Sn)S crystals is predicted to outperform most of the current state-of-the-art thermoelectric sulfide materials.