Large and persistent photoconductivity (LPPC) in semiconductors is due to the trapping of photo-generated minority carriers at crystal defects. Theory has suggested that anion vacancies in II-VI semiconductors are responsible for LPPC due to negative-U behavior, whereby two minority carriers become kinetically trapped by lattice relaxation following photo-excitation. By performing a detailed analysis of photoconductivity in CdS, we provide experimental support for this negative-U model of LPPC. We also show that LPPC is correlated with sulfur deficiency. We use this understanding to vary the photoconductivity of CdS films over nine orders of magnitude, and vary the LPPC characteristic decay time from seconds to 10^4 seconds, by controlling the activities of Cd^{2+} and S^{2-} ions during chemical bath deposition. We suggest a screening method to identify other materials with long-lived, non-equilibrium, photo-excited states based on the results of ground-state calculations of atomic rearrangements following defect redox reactions, with a conceptual connection to polaron formation.