We analyze a nitrogen-vacancy (NV^-) colour centre based single photon source based on cavity Purcell enhancement of the zero phonon line and suppression of other transitions. Optimal performance conditions of the cavity-centre system are analyzed using Master equation and quantum trajectory methods. By coupling the centre strongly to a high-finesse optical cavity [Q ~ O(10^4-10^5), V ~ lambda^3] and using sub-picosecond optical excitation the system has striking performance, including effective lifetime of 70 ps, linewidth of 0.01 nm, near unit single photon emission probability and small [O(10^-5)] multi-photon probability.
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