Tidal interactions within binary stars circularize eccentric orbits in shorter period systems. The distribution of orbital eccentricity with periods of binary stars in open clusters and other coeval populations show a distinct transition between short-period circular orbits and long-period eccentric orbits. This circularization period, and its dependence on cluster age, places important constraints on current tidal circularization theories. Previous studies of circularization periods in open clusters have employed Monte Carlo simulations to determine the circularization periods and associated uncertainties. In this work, we use orthogonal distance regression to determine circularization period uncertainties and a statistical bootstrap method to derive a distribution of circularization periods for solar-like main-sequence binaries in clusters ranging in age from ~3 Myr to ~10 Gyr. In particular, we update measured circularization periods in the clusters M35, NGC 6819, M67, NGC 188, and the Hyades as well as in the field and halo binary populations. We also present preliminary results from the WIYN Open Cluster Study radial-velocity survey of NGC 2506 of over 9000 measurements of nearly 2600 stars, including likely cluster members from both the radial-velocity data and Gaia proper motions, orbital solutions. We use our new methodology to estimate the NGC 2506 tidal circularization period for the first time. The authors acknowledge funding support from NSF AST- 1714506. The authors gratefully acknowledge the many Wisconsin undergraduate and graduate students who have contributed to the WIYN Open Cluster Study radial-velocity database.