We have examined the light curves of the planetary nebulae (PNe) in all Kepler/K2 campaigns (0 through 19) to identify central star (CS) variability that may indicate a binary CS. We found no variable CS among the three PNe in Campaign 0, but we did identify one likely variable among the four PNe in Campaign 2, three variables among the 12 PN candidates in Campaign 7, one possible variable in the single PN in Campaign 15, and one very likely binary CS in the only PN in Campaign 16 (Abell 30). Our primary effort, though, was focused on Campaign 11 which targeted a Galactic bulge field having approximately 183 PNe in which we identified 21 strong candidate variable CS, plus another 9 possible, but less convincing, variables. The periods of our variables range from 2.3h to 30d. Most of the variables are likely to be binary stars. From our sample of 204 target PNe, we find the fraction of PNe having a binary (or, at least variable) CS to be 20-25 percent, depending on the selected subsample (e.g., all PN candidates or only `true' PNe) and details of the incompleteness correction. We believe that these fractions are lower limits for various reasons, primarily due to reduced sensitivity to detecting variability caused by dilution and noise from the nebula and neighbouring stars. This degradation is especially severe for longer period, highly separated systems.