The Hubble Space Telescope/Advanced Camera for Surveys (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 6.5-m Monolithic Mirror Telescope (MMT). Among the many scientific applications for these data is 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 samples should be classified as compact ellipticals or M32-like galaxies, and the remaining four being less extreme systems. The three compact ellipticals are all found to have old luminosity weighted ages (>~12 Gyr), intermediate metallicities (-0.6 < [Fe/H] < -0.1) and high [Mg/Fe] (>~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.