It is unlikely that X-rays could produce an inverted population in the nuclei of Cobalt atoms. However neutrons would be absorbed by the cobalt nuclei to make a high energy state. This would decay with a particular half life to the ground state with the emission of a gamma photon.
If a high flux of neutrons bombarded the cobalt nuclei then an inverted high energy population would occur. Gaser action would make a high intensity gamma ray beam to make the device useful.
To make the neutron flux a chain reaction from uranium 235 could be used. A critical mass of Uranium 235 with a moderator core would be used. The moderator of Graphite would be momentarily removed and quickly replaced to give a burst of neutrons.
The geometry would be a cobalt bar with a uranium 235 core with a moderator rod of graphite down the center. To fire the device the graphite rod would be briefly removed with a mechanical or gas trigger and then quickly replaced.
The Uranium would go critical briefly and soak the cobalt with neutrons making an inverted population of high energy cobalt nuclei. Gaser action would result in a beam of gamma photons.
The business end would be open and point at the target while the opposite end would be closed with graphite. The whole device except the business end would be shielded with graphite tube surrounded be lead to protect the operator.
Just a Suggestion!
Chris.