We report crystal structure, magnetization, and specific heat measurements on single crystals of the hexagonal polar magnet magnetically diluted by replacing Co by Zn. In contrast to the transformation from the antiferromagnetic to a ferrimagnetic state observed in the isostructural upon small Zn doping, a robust antiferromagnetic behavior is preserved in Zn-doped up to . The Néel temperature decreases from K at to 23 K at , thus extrapolating to (36% filling) as the percolation threshold typical for a three-dimensional, highly coordinated network. This indicates strong magnetic couplings beyond the honeycomb planes in . 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 , whereas at these features are broadened due to increased disorder. Interestingly, the in-plane lattice parameter, the Curie-Weiss temperature, and the magnetic entropy vary with 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 () 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 ions, this behavior is reflected in the nonmonotonic variation of the Curie-Weiss temperature and magnetic entropy with substitution.