This paper presents photometric redshifts for 431 Abell clusters imaged as part of the Palomar Abell Cluster Optical Survey (PACOS), of which 236 are new redshi fts. We have obtained moderately deep, 3--band (Gunn gri) imaging for this sam ple at the Palomar Observatory 60'' telescope, as part of the photometric calibration of DPOSS. Our data acquisition, reduction, and photometric calibration techniques are described, and photometric accuracy and consistency is demonstrated. An empirical redshift estimator is presented, utilizing background-corrected median g-r colors and mean g magnitudes for the ensemble of galaxies in each field. We present photometric redshift estimates for the clusters in our sample with an accuracy of sigma_z=0.038. These redshift estimates provide checks on single-galaxy cluster redshifts, as well as distance information for studies of the Butcher-Oemler effect, luminosity functions, M/L ratios, and many other projects. ; Comment: 21 pages, including 5 figures Accepted to AJ