  We describe a new transit detection algorithm designed to detect single
transit events in discontinuous Perkins INfrared Exosatellite Survey (PINES)
observations of L and T dwarfs. We use this algorithm to search for transits in
131 PINES light curves and identify two transit candidates: 2MASS
J18212815+1414010 (2MASS J1821+1414) and 2MASS J08350622+1953050 (2MASS
J0835+1953). We disfavor 2MASS J1821+1414 as a genuine transit candidate due to
the known variability properties of the source. We cannot rule out the
planetary nature of 2MASS J0835+1953's candidate event and perform follow-up
observations in an attempt to recover a second transit. A repeat event has yet
to be observed, but these observations suggest that target variability is an
unlikely cause of the candidate transit. We perform a Markov chain Monte Carlo
simulation of the light curve and estimate a planet radius ranging from
$4.2^{+3.5}_{-1.6}R_\oplus$ to $5.8^{+4.8}_{-2.1}R_\oplus$, depending on the
host's age. Finally, we perform an injection and recovery simulation on our
light curve sample. We inject planets into our data using measured M dwarf
planet occurrence rates and attempt to recover them using our transit search
algorithm. Our detection rates suggest that, assuming M dwarf planet occurrence
rates, we should have roughly a 1$\%$ chance of detecting a candidate that
could cause the transit depth we observe for 2MASS J0835+1953. If 2MASS
J0835+1953 b is confirmed, it would suggest an enhancement in the occurrence of
short-period planets around L and T dwarfs in comparison to M dwarfs, which
would challenge predictions from planet formation models.
