Recently, it was found that the soft X-ray excess in the center of Coma can be explained by axion to photon conversion of a cosmic axion background (CAB). We extend this analysis to the outskirts of Coma, including regions up to 5 Mpc from the center of the cluster. We extract the soft X-ray flux from ROSAT All-Sky Survey data and compare it to the expected flux from axion to photon conversion of a CAB. The soft X-ray excess both in the center and the outskirts of Coma can be simultaneously explained by axion to photon conversion of a CAB. Given the uncertainties of the cluster magnetic field in the outskirts we constrain the parameter space of the CAB. In particular, an upper limit on the CAB mean energy and a range of allowed axion photon couplings are derived.