Paramagnetic color centers in hexagonal boron nitride (h-BN) are promising candidates for quantum technologies due to their potential for stable single-photon emission. However, identifying the precise atomic configurations responsible for such emission remains a challenge. Using hybrid density functional theory, we show that a defect complex formed by carbon substitution at the nitrogen site combined with a Stone-Wales defect (CN + SW) in h-BN gives rise to a single-photon emitter near the 4 eV photoluminescence line. The calculated Huang-Rhys factor of ~1.9 indicates moderate electron-phonon coupling, while the strong transition dipole moment (0.94 eÅ) and short radiative lifetime (1.92 ns) suggest efficient optical transitions. To compute and analyze these optical properties, we employed the DEFECTPL Python package, which implements the generating function approach for modeling defect-related luminescence. DEFECTPL enables the calculation of key photophysical parameters such as the Huang-Rhys factor, Debye-Waller factor, photoluminescence spectra, and electron-phonon spectral functions, and includes the effects of isotopic substitution. The excellent agreement between our theoretical predictions and experimental observations of carbon-related emitters in h-BN highlights both the viability of the CN + SW defect and the utility of DEFECTPL as a tool for defect-based quantum emitter discovery.