ATHENA-C is a homogeneous grid of radiative-transfer models for carbon-rich asymptotic giant branch (AGB) stars. The models combine COMARCS hydrostatic stellar atmospheres with the DUSTY radiative-transfer code to self-consistently describe the stellar photosphere and the surrounding dusty circumstellar envelope. The grid spans a wide range of stellar and circumstellar parameters, including effective temperature, luminosity, carbon-to-oxygen ratio, dust optical depth, and wind prescriptions. It is designed for spectral energy distribution (SED) fitting and population studies. This dataset is intended for use in observational studies of carbon-rich AGB stars and is released alongside the accompanying publication.