We report the results of a diffraction-limited, photometric variability study of the central 5\tt'' * 5\tt'' of the Galaxy conducted over the past 10 years using speckle imaging techniques on the W. M. Keck I 10 m telescope. Within our limiting magnitude of m_K < 16 mag for images made from a single night of data, we find a minimum of 15 K[2.2 micron ]-band variable stars out of 131 monitored stars. While large populations of binaries have been posited to exist in this region, both to explain the presence of young stars in the vicinity of a black hole and because of the high stellar densities, only two binaries are identified in this study. First is the previously identified Ofpe/WN9 equal mass eclipsing binary star IRS 16SW, for which we measure an orbital period of 19.448 +/- 0.002 days. In contrast to recent results, our data on IRS 16SW show an asymmetric phased light curve with a much steeper fall-time than rise-time, which may be due to tidal deformations caused by the proximity of the stars in their orbits. Second is the WC 9 Wolf-Rayet star IRS 29N; its observed photometric variation over a few year time-scale is likely due to episodic dust production in a binary system containing two windy stars. Our sample also includes 4 candidate Luminous Blue Variable (LBV) stars (IRS 16NE, 16C, 16NW, 16SW). While 2 of them show variability, none show the characteristic of LBVs large increase or decrease in luminosity. However, our time baseline is too short to rule them out as LBVs. Nonetheless, the lack of evidence for these stars to be LBVs and their coexistence with a significant surrounding population of well established Wolf-Rayet stars is consistent with needing only a single recent starburst event at the Galactic center to account for all of the known, young, massive stars. Among the remaining variable stars, the majority are early-type stars and three are possibly variable due to line of sight extinction variations. For the 7 OB stars at the center of our field of view that have well- determined 3-dimensional orbits, we see no evidence of flares or dimming of their light, which limits the possibility of a cold, geometrically-thin inactive accretion disk around the supermassive black hole, Sgr A*.