  We present a systematic search for periodically varying quasars and
supermassive black hole binary (SMBHB) candidates in the Pan-STARRS1 (PS1)
Medium Deep Survey's MD09 field. From a color-selected sample of 670 quasars
extracted from a multi-band deep-stack catalog of point sources, we locally
select variable quasars and look for coherent periods with the Lomb-Scargle
periodogram. Three candidates from our sample demonstrate strong variability
for more than ~3 cycles, and their PS1 light curves are well fitted to
sinusoidal functions. We test the persistence of the candidates' apparent
periodic variations detected during the 4.2 years of the PS1 survey with
archival photometric data from the SDSS Stripe 82 survey or new monitoring with
the Large Monolithic Imager at the Discovery Channel Telescope. None of the
three periodic candidates (including PSO J334.2028+1.4075) remain persistent
over the extended baseline of 7 - 14 years, corresponding to a detection rate
of < 1 in 670 quasars in a search area of 5 deg^2. Even though SMBHBs should be
a common product of the hierarchal growth of galaxies, and periodic variability
in SMBHBs has been theoretically predicted, a systematic search for such
signatures in a large optical survey is strongly limited by its temporal
baseline and the "red noise" associated with normal quasar variability. We show
that follow-up long-term monitoring (>5 cycles) is crucial to our search for
these systems.
