The HST ACS Coma Cluster Treasury Survey is a deep two passband imaging survey of the nearest very rich cluster of galaxies , covering a range of galaxy density environments . The imaging is complemented by a recent wide field redshift survey of the cluster conducted with Hectospec on the 6.5m MMT . Among the many scientific applications for this data are the search for compact galaxies . In this paper , we present the discovery of seven compact ( but quite luminous ) stellar systems , ranging from M32-like galaxies down to ultra-compact dwarfs ( UCDs ) /dwarf to globular transition objects ( DGTOs ) . We find that all seven compact galaxies require a two-component fit to their light profile and have measured velocity dispersions that exceed those expected for typical early-type galaxies at their luminosity . From our structural parameter analysis we conclude that three of the sample should be classified as compact ellipticals or M32-like galaxies , the remaining four being less extreme systems . The three compact ellipticals are all found to have old luminosity weighted ages ( \gtrsim 12 Gyr ) , intermediate metallicities ( -0.6 < [ Fe/H ] < -0.1 ) and high [ Mg/Fe ] ( \gtrsim 0.25 ) . Our findings support a tidal stripping scenario as the formation mode of compact galaxies covering the luminosity range studied here . We speculate that at least two early-type morphologies may serve as the progenitor of compact galaxies in clusters .