We have searched for the two-photon production of the /eta//sub c/, /chi//sub 0/ and /chi//sub 2/ charmonium states at the e/sup +/e/sup -/ collider PEP in the channels /gamma//gamma/ /yields/ K/sup +-/K/sub S//sup 0//pi//sup -+/, /gamma//gamma/ /yields/ K/sup +/K/sup -//pi//sup +//pi//sup -/, /gamma//gamma/ /yields/ /pi//sup +//pi//sup -//pi//sup +//pi//sup -/ and /gamma//gamma/ /yields/ K/sup +/K/sup -/K/sup +/K/sup -/. We identify four /eta//sub c/ candidates in the K/sup +/K/sup -/K/sup +/K/sup -/ channel, on a negligible background; this leads to a preliminary 95% C.L. lower limit for /Gamma//sub /gamma//gamma//(/eta//sup c/) of 1.6 keV. In the other channels we find no evidence for any of the three states and establish preliminary 95% C.L. upper limits /Gamma//sub /gamma//gamma//(/eta//sub c/) < 15 keV, /Gamma//sub /gamma//gamma//(/chi//sub 0/)< 14 keV and /Gamma//sub /gamma//gamma//(/chi//sub 2/) < 4.0 keV. Combining the results on the /eta//sub c/ from all channels we obtain the value /Gamma//sub /gamma//gamma//(/eta//sub c/) = 4.5/sub -3.6///sup -5.5 keV. 18 refs., 3 figs., 1 tab.