We report crystal structure, magnetization, and specific heat measurements on single crystals of the hexagonal polar magnet Co2-xZnxMo3O8 magnetically diluted by replacing Co by Zn. In contrast to the transformation from the antiferromagnetic to a ferrimagnetic state observed in the isostructural Fe2Mo3O8 upon small Zn doping, a robust antiferromagnetic behavior is preserved in Zn-doped Co2Mo3O8 up to x=0.55. The Néel temperature decreases from TN=40 K at x=0 to 23 K at x=0.55, thus extrapolating to x=1.27 (36% filling) as the percolation threshold typical for a three-dimensional, highly coordinated network. This indicates strong magnetic couplings beyond the honeycomb planes in Co2Mo3O8. A sharp peak in the specific heat and a clear cusp in the susceptibility associated with the onset of magnetic order is observed up to x=0.55, whereas at x=0.66 these features are broadened due to increased disorder. Interestingly, the in-plane lattice parameter, the Curie-Weiss temperature, and the magnetic entropy vary with x in a concerted but nonmonotonic manner. These observations can be traced back to the observed site-selective Zn substitution. We found that in the low-doping regime (x<0.2) Zn2+ ions primarily occupy the octahedrally coordinated sites, although they have a clear preference for occupying the tetrahedrally coordinated sites at higher doping levels. Due to the multiple interlayer exchange paths, dependent on the coordination of the Co2+ ions, this behavior is reflected in the nonmonotonic variation of the Curie-Weiss temperature and magnetic entropy with substitution.