In this paper we present the results of searches for periodic neutrino
emission from a catalog of binary systems. Such modulation, observed in the
photon flux, would be caused by the geometry of these systems. In the analysis,
the period is fixed by these photon observations, while the phase and duration
of the neutrino emission are treated as free parameters to be fit with the
data. If the emission occurs during ~20% or less of the total period, this
analysis achieves better sensitivity than a time-integrated analysis. We use
the IceCube data taken from May 31, 2007 to April 5, 2008 with its 22-string
configuration, and from April 5, 2008 to May 20, 2009 with its 40-string
configuration. No evidence for neutrino emission is found, with the strongest
excess occurring for Cygnus X-3 at 2.1 sigma significance after accounting for
trials. Neutrino flux upper limits for both periodic and time-integrated
emission are provided.