Quantum communication places stringent requirements on single-photon sources. Here we report a theoretical study of the cavity Purcell enhancement of two diamond point defects, the nickel-nitrogen (NE8) and silicon-vacancy (SiV) centers, for high-performance, near on-demand single-photon generation. By coupling the centers strongly to high-finesse optical photonic-bandgap cavities with modest quality factor Q = O(10^4) and small mode volume V = O(lambda^3), these system can deliver picosecond single-photon pulses at their zero-phonon lines with probabilities of 0.954 (NE8) and 0.812 (SiV) under a realistic optical excitation scheme. The undesirable blinking effect due to transitions via metastable states can also be suppressed with O(10^{-4}) blinking probability. We analyze the application of these enhanced centers, including the previously-studied cavity-enhanced nitrogen-vacancy (NV) center, to long-distance BB84 quantum key distribution (QKD) in fiber-based, open-air terrestrial and satellite-ground setups. In this comparative study, we show that they can deliver performance comparable with decoy state implementation with weak coherent sources, and are most suitable for open-air communication.