We use a high-temperature chemical network to derive the molecular abundances in axisymmetric accretion disk models around active galactic nuclei (AGNs) within 100 pc using simple radial and vertical density and temperature distributions motivated by more detailed physical models. We explore the effects of X-ray irradiation and cosmic ray ionization on the spatial distribution of the molecular abundances of CO, CN, CS, HCN, HCO+, HC3N, C2H, and c-C3H2 using a variety of plausible disk structures. These simple models have molecular regions with a layer of X-ray dominated regions, a midplane without the strong influence of X-rays, and a high-temperature region in the inner portion with moderate X-ray flux where families of polyynes (C$_{rm n}$H$_{2}$) and cyanopolyynes can be enhanced. For the high midplane density disks we explore, we find that cosmic rays produced by supernovae do not significantly affect the regions unless the star formation efficiency significantly exceeds that of the Milky Way. We highlight molecular abundance observations and ratios that may distinguish among theoretical models of the density distribution in AGN disks. Finally, we assess the importance of the shock crossing time and the accretion time relative to the formation time for various chemical species. Vertical column densities are tabulated for a number of molecular species at both the characteristic shock crossing time and steady state. Although we do not attempt to fit any particular system or set of observations, we discuss our models and results in the context of the nearby AGN NGC 1068.
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