Nanoparticles of the diluted magnetic semiconductor Cd0.991Co0.009S, with diameters D between 3.5 and 29.5 nm, were studied by Cd-113 NMR spectroscopy. Two spectral features could be discerned: (1) a strong line corresponding to cadmium atoms that are removed more than four bonds from cobalt ions and (2) a set of shifted lines resulting from transferred hyperfine (THF) interactions between the d-electrons of Co2+ and its next nearest (2N) neighboring cadmium atoms. Significant changes in the Cd-113 spectrum were observed as a function of the size of the nanoparticles. More specifically, these changes were attributed to a structural zinc blende-to-wurtzite phase transition that occurs around D = 8 nm. The frequency spread and the fine structure of the spectra indicate that most of the Co2+ impurities in the crystals are located at the positions of cadmium sites. These paramagnetic ions are distributed homogeneously in the samples and the transferred hyperfine interactions between the d-electrons of cobalt and the 2N Cd-113 nuclei are of the same order of magnitude as in bulk samples. Inhomogeneous broadening of the lines in the spectra can be attributed to possible distortions of the electronic polarization pathways because of surface and local disorder effects in the nanocrystals.