Planets in Stellar Clusters Extensive Search. III. A search for transiting planets in the metal-rich open cluster NGC 6791

We have undertaken a long-term project, Planets in Stellar Clusters Extensive Search (PISCES), to search for transiting planets in open clusters. In this paper we present the results for NGC 6791 -- a very old, populous, metal rich cluster. We have monitored the cluster for over 300 hours, spread over 84 nights. We have not detected any good transiting planet candidates. Given the photometric precision and temporal coverage of our observations, and current best estimates for the frequency and radii of short-period planets, the expected number of detectable transiting planets in our sample is 1.5. We have discovered 14 new variable stars in the cluster, most of which are eclipsing binaries, and present high precision light curves, spanning two years, for these new variables and also the previously known variables.