  Detection of transiting exoplanets around young stars is more difficult than
for older systems due to increased stellar variability. Nine young open cluster
planets have been found in the K2 data, but no single analysis pipeline
identified all planets. We have developed a transit search pipeline for young
stars which uses a transit-shaped notch and quadratic continuum in a 12 or
24\,hour window to fit both the stellar variability and the presence of a
transit. In addition, for the most rapid rotators (P$_\mathrm{rot}<2$\,days) we
model the variability using a linear combination of observed rotations of each
star. To maximally exploit our new pipeline, we update the membership for four
stellar populations observed by K2 (Upper Scorpius, Pleiades, Hyades,
Praesepe), and conduct a uniform search of the members. We identify all known
transiting exoplanets in the clusters, 17 eclipsing binaries, one transiting
planet candidate orbiting a potential Pleiades member, and three orbiting
unlikely members of the young clusters. Limited injection-recovery testing on
the known planet hosts indicates that for the older Praesepe systems, we are
sensitive to additional exoplanets as small as 1-2\,R$_\oplus$, and for the
larger Upper Scorpius planet host (K2-33) our pipeline is sensitive to
$\sim$4\,R$_\oplus$ transiting planets. The lack of detected multiple systems
in the young clusters is consistent with the expected frequency from the
original Kepler sample, within our detection limits. With a robust pipeline
that detects all known planets in the young clusters, occurrence rate testing
at young ages is now possible.
