High-repetition-rate sources of bright electron bunches have a wide range of applications. They can directly be employed as probes in electron-scattering setups, or serve as a backbone for the generation of radiation over a broad range of the electromagnetic spectrum. This paper describes the development of a compact sub-Mega-electronvolt (sub-MeV) electron-source setup capable of operating at MHz repetition rates and forming sub-picosecond electron bunches with transverse emittance below 20~nm. The setup relies on a conduction-cooled superconducting single-cell resonator with its geometry altered to enhance the field at the surface of the emitter. The system is designed to accommodate cooling using a model a $2$~W at 4.2 K pulse tube cryogen-free cryocooler. Although we focus on the case of a photoemitted electron bunch, the scheme could be adapted to other emission mechanisms.
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