A systematic molecular coarse-graining (CG) approach for aqueous polyelectrolyte solutions is presented with sodium polystyrenesulfonate (NaPSS) with different chain tacticities as example systems. The styrenesulfonate repeat unit is mapped on a three-site CG representation with the counterion being modeled explicitly while the solvent is modeled implicitly. The CG force field discriminates between bonded and nonbonded forces, which have been developed independently. The bonded interactions correspond to the potentials of mean force of CG bond, angle, and torsion degrees of freedom obtained from sampling isolated chains with an atomistic force field that includes only the local interactions along the chain. The nonbonded interactions correspond to bead-bead potentials of mean force, obtained from simulations of small molecule or ion pairs in explicit water. The CG model reproduces the local and global conformations of polyelectrolyte chains in good agreement with the parent atomistic chains in aqueous solution. By using a relative dielectric permittivity based on the local concentration of counterions around the polyelectrolyte chain, the quality of our CG models can be further improved substantially. The effect of added salt (NaCl) on the radius of gyration of PSS chains with different tacticities has also been studied and results show the transferability of the CG NaPSS model to regimes with different electrostatic conditions. We furthermore show that the CG procedure presented here can easily be extended to CG models for partially sulfonated polystyrene systems.