  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 9 stars from 6 fields. Since our sample
is flux-limited, it is strongly biased towards 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 (LSP). We use a
Monte Carlo (MC) algorithm to yield robust analysis of the statistical
significance of cycle detections and non-detections. None of the 9 stellar
lightcurves 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.
