The phase diagram of a two-flavor Polyakov-loop Nambu.Jona-Lasinio model is analyzed imposing the constraint of color charge neutrality. The main effect of this constraint is a coexistence of the chiral symmetry breaking (χSB) and two-flavor superconducting phases. Additional effects are a shrinking of the χSB domain in the T-μ plane and a shift of the end point to lower temperatures, but their quantitative importance is shadowed by the intrinsic uncertainties of the model. The effects can be understood in view of the presence of a nonvanishing color chemical potential μ₈, which is introduced to compensate the color charge density ρ₈ induced by a background color gauge mean field φ₃. At low temperatures and large chemical potentials the model exhibits a quarkyonic phase, which gets additional support from the diquark condensation.