In this second paper of the series, observational results of our spectroscopic survey of Seyfert galaxies in the near-infrared are presented, and the potential for using emission-line ratios in this spectral region as a classification diagnostic tool is examined. Near-infrared CCD spectra, which cover the range lambda-lambda-7000-10000 at nominal resolution FWHM almost-equal-to 12 angstrom, of 15 additional Seyferts and two starburst galaxies were obtained with the Lick Observatory 3 m Shane telescope. Relative emission-line intensities from these observations, in combination with measurements from our first paper (Osterbrock, Shaw, & Veilleux) and those of Morris & Ward as well as additional Lick observations and measurements of new, high signal-to-noise ratio optical spectra of many of these objects, are used to study the diagnostic diagrams involving [S III] lambda-lambda-9069, 953t/H-alpha, [O II] lambda-lambda-7320, 7330/H-alpha, [S II] lambda-lambda-6716, 6731/H-alpha, and [O III] lambda-5007/H-beta. Comparisons are made in these diagrams between observational data from the active galaxies and published measurements of H II region-like objects, as well as with predictions from simple one-component models calculated for the two types of objects. Our results suggest that diagnostic diagrams using near-IR lines such as [O II] lambda-lambda-7320, 7330 and [S III] lambda-lambda-9069, 9531 promise to provide a powerful method in classifying emission-line galaxies. Most but not all the diagnostic diagrams can be understood on the basis of photoionization models. There may be some heating due to relativistic electrons in addition to photoionization in active galactic nuclei (AGNs), but this is not at all clear.