Stellar activity cycles are known to be a widespread phenomenon amongst moderately active solar- and late-type stars from long-term periodic variations in chromospheric Ca II H and K emission lines, yet to date, only a handful of coronal X-ray cycles are known. We have surveyed serendipitously observed stellar sources in fields observed multiple times in the last decade by XMM-Newton and present our analysis of nine stars from six fields. Since our sample is flux-limited, it is strongly biased toward higher levels of X-ray activity. We fit a single temperature APEC spectrum to each source and search for significant periodicities using a Lomb-Scargle periodogram. We use a Monte Carlo (MC) algorithm to yield robust analysis of the statistical significance of cycle detections and non-detections. None of the nine stellar light curves show any convincing indications of periodicity. From MC simulations, we simulate the detection capabilities of our methodology and, assuming a uniform distribution of cycle periods and strengths over the domain searched, we conclude with 95% confidence that less than 72% of the stars represented by our sample of active stars have 5-13 year coronal X-ray cycles.