Many model studies of proton tunneling in condensed phase employ a reaction coordinate that is coupled to a bath of harmonic oscillator modes. The nature of the coupled modes and the effect of the coupling parameters on reaction rate is an active area of investigation. Recent experimental results from the Fleming group showed that the spectral density for solvation can be temperature dependent [A. Passino, Y. Nagasawa, and G. R. Fleming, J. Chem. Phys. 107, 6094 (1997)]. Translated from the Langevin picture, this result implies that bath modes are anharmonic, or that a different set of harmonic modes are needed at each temperature. In addition, calculations of proton transfer rates have shown that quantum dynamics can be significantly affected by the variation of spectral densities in the low frequency regime [D. Antoniou and S. D. Schwartz, J. Chem. Phys. 109, 5487 (1998)]. We report a study of proton transfer in which the reaction coordinate is coupled to a Morse oscillator with nonlinear coupling. Comparison with the case of coupling to a harmonic oscillator shows that coupling a Morse oscillator to the reaction coordinate leads to enhanced tunneling. We compare our results with those reported in an earlier study [Y. Dakhnovskii, B. Bursulaya, and H. J. Kim, J. Chem. Phys. 102, 7838 (1995)], where the rate of proton tunneling coupled to a one-dimensional classical anharmonic mode was studied.