We used a sequence of velocity-modulated photographs to find and measure the radial velocities of faint planetary nebulae in the center of M31. The photographs were made with a Velocity Modulating Camera (VMC) which consists of a temperature-tuned 2.1 Å (FWHM) (O III) λ 5007 interference filter, a cooled, two-stage image intensifier, and a calibrating photomultiplier. The camera was mounted at the Cassegrain focus of the Shane 3 m telescope at Lick Observatory. We identified 19 new planetary nebulae, bringing the total number of known planetaries within 250 pc of M31's nucleus to 45. From the plate series, we derived radial velocities and relative brightnesses from 32 of the nebulae and placed radial velocity limits on the remaining nebulae in the field. By applying the method of maximum likelihood to the observed radial velocity distribution, we derive a mean heliocentric velocity of −309 (±25) km s−1 and a velocity dispersion of 155 (±22) km s−1 for the planetary nebulae.