Solid-state single-photon sources (SPS) based on quantum dots as well as color centers in diamonds and silicon-carbide have promise for application in emerging quantum technologies. Many of these technologies, however, demand photon rates in the GHz range, thereby hindering the use of these SPS, for which the maximum observed count rates are limited to a few tens of MHz. Here we first study the performance of hyperbolic metamaterial-based 5-layered metal–dielectric resonator antenna structures with metallic as well as hybrid metal–dielectric antennas in the wavelength range of 600 to 1000 nm. The performance of these resonator-antenna structures was analyzed for the Purcell enhancement, quantum efficiency (QE), collection efficiency (CE), and normalized collected photon counts (NCPC). The hybrid metal–dielectric antenna helps in providing the directivity to the dipole emission, thereby significantly improving the collection efficiency. We then present the novel design of a 5-layered metal–dielectric pillar resonator. This resonator structure with a metallic cylindrical antenna over the top showed significantly large fluorescence enhancement values. The Purcell factor was observed to reach close to 1600 at 680 nm corresponding to the central peak of the nitrogen vacancy center spectrum. The NCPC value reached close to 550 at 680 nm. The maximum CE from the structure was observed to be around 60%, with the maximum QE reaching close to 80%. With the above performance, the detected photon count rates for a solid-state SPS is expected to be well into the GHz range. Our designs show a state-of-the-art improvement in the antenna performance for SPS with properties very close to a practical SPS.