Six planetary nebulae (PN) are known in the Kepler space telescope field of view, three of which are newly identified. Of the five central stars of PN with useful Kepler data, one, J193110888+4324577, is the first short-period, post-common envelope binary exhibiting relativistic beaming effects. A second, the central star of the newly identified PN Pa 5, has a rare O(He) spectral type and a periodic variability consistent with an evolved companion, where the orbital axis is almost aligned with the line of sight. The third PN, NGC 6826, has a fast rotating central star, something that can only be achieved in a merger. Fourth, the central star of the newly identified PN Kn 61, has a PG1159 spectral type and a mysterious semi-periodic light variability which we conjecture to be related to the interplay of binarity with a stellar wind. Finally, the central star of the circular PN A61 does not appear to have a photometric variability above 2 mmag. With the possible exception of the variability of Kn 61, all other variability behaviour, would not easily have been detected from the ground. We conclude, based on very low numbers, that there may be many more close binary or close binary products to be discovered with ultra-high-precision photometry. With a larger number of high-precision photometric observations, we will be able to determine how much higher than the currently known 15 per cent, the short-period binary fraction for central stars of PN is likely to be.