Photoinduced second harmonic generation (PISHG) in undoped as well as in various Cu-doped (0.05-1.2% Cu) CdI2 nanocrystals was measured at liquid nitrogen temperature (LNT). It was found that the PISHG increases with increasing Cu doping up to similar to 0.6% and then decreases almost to that for the undoped CdI2 for doping higher than similar to 1%. The values of the second-order susceptibility ranged from 0.50 to 0.67 pm V-1 for the Cu-doped nanocrystals with a thickness of 0.5 nm. The Cu-doping dependence shown in a parabolic fashion suggests a crucial role of the Cu agglomerates in the observed effects. The PISHG in crystals with various nanosizes was also measured at LNT. The size dependence demonstrated the quantum-confined effect with a maximum PISHG for 0.5 nm and with a clear increase in the PISHG with decreasing thickness of the nanocrystal. The Raman scattering spectra at different pumping powers were taken for thin nanocrystals, and the phonon modes originating from interlayer phonons were observed in the spectra. The results were discussed within a model of photoinduced electron-phonon anharmonicity.