We present a source catalog from a deep 26ks Galaxy Evolution Explorer (GALEX) observation of the Coma cluster in the far-UV (FUV; 1530{AA}) and near-UV (NUV; 2310{AA}) wavebands. The observed field is centered ~0.9{deg} (1.6Mpc) southwest of the Coma core in a well-studied region of the cluster known as "Coma-3". The entire field is located within the apparent virial radius of the Coma cluster, and has optical photometric coverage with Sloan Digital Sky Survey (SDSS) and deep spectroscopic coverage to r~21. We detect GALEX sources to NUV=24.5 and FUV=25.0, which corresponds to a star formation rate of ~10^-3^M_{sun}_/yr for galaxies at the distance of Coma. We have assembled a catalog of 9700 galaxies with GALEX and SDSS photometry, including 242 spectroscopically confirmed Coma member galaxies (in fig. 1) that span a large range of galaxy types from giant spirals and elliptical galaxies to dwarf irregular and early-type galaxies. The full multi-wavelength catalog (cluster plus background galaxies) is ~80% complete to NUV=23 and FUV=23.5. The GALEX images presented here are very deep and include detections of many resolved cluster members superposed on a dense field of unresolved background galaxies.