The development, characterization and control of $N$-photon sources are instrumental for quantum technological applications. This work constitutes a step forward in this direction, where we propose a cavity quantum electrodynamics setup designed for the generation of photon pairs. We analyze it both via the scattering and master equation formalisms. From the connection between these two frameworks it naturally arises a physical criterion characterizing when weakly-driven systems behave as continuous antibunched two-photon sources. We find the optimal parameters for which our setup works as an efficient photon-pair source, showing also that it becomes a deterministic down-converter of single photons. We provide a specific implementation based on state-of-the-art superconducting circuits, showing how our proposal is within the reach of current technologies.
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