  The Galactic center has some of the highest stellar densities in the Galaxy
and a range of interstellar scattering properties that may aid in the detection
of new radio-selected transient events. Here we describe a search for radio
transients in the Galactic center using over 200 hours of archival data from
the Very Large Array (VLA) at 5 and 8.4 GHz. Every observation of SgrA* from
1985$-$2005 has been searched using an automated processing and detection
pipeline sensitive to transients with timescales between 30 seconds and five
minutes with a typical detection threshold of $\sim$100 mJy. Eight possible
candidates pass tests to filter false-positives from radio-frequency
interference, calibration errors, and imaging artifacts. Two events are
identified as promising candidates based on the smoothness of their light
curves. Despite the high quality of their light curves, these detections remain
suspect due to evidence of incomplete subtraction of the complex structure in
the Galactic center, and apparent contingency of one detection on reduction
routines. Events of this intensity ($\sim$100 mJy) and duration ($\sim$100 s)
are not obviously associated with known astrophysical sources, and no
counterparts are found in data at other wavelengths. We consider potential
sources, including Galactic center pulsars, dwarf stars, sources like GCRT
J1745-3009, and bursts from X-ray binaries. None can fully explain the observed
transients, suggesting either a new astrophysical source or a subtle imaging
artifact. More sensitive multiwavelength studies are necessary to characterize
these events which, if real, occur with a rate of $14^{+32}_{-12}~{\rm
hr}^{-1}\,{\rm deg}^{-2}$ in the Galactic center.
