Monolithic integration of solid-state emitters with photonic elements of the same material is a promising approach to overcome the constraints of fabrication complexity and coupling losses in traditional hybrid integration approaches. A wide band gap, low-loss silicon nitride (SiN) platform is a mature technology, having CMOS compatibility, widely used in hybrid integrated photonics and optoelectronics. However, it has been shown that certain growth conditions enable the SiN material to host color centers, whose origin is currently under investigation. In this work, we have engineered a novel technique for the efficient coupling of these intrinsic emitters into the whispering gallery modes (WGMs) of the SiN microring cavity, which has not been explored previously. We have engineered a subwavelength-sized notch into the rim of the SiN microring structure to optimize the collection efficiency of the cavity-coupled enhanced photoluminescence (PL) spectra at room temperature. The platform presented in this work will enable the development of the monolithic integration of color centers with nanophotonic elements for application to quantum photonic technologies.