Resonant excitation of solid-state quantum emitters enables coherent control of quantum states and generation of coherent single photons, which are required for scalable quantum-photonics applications. However, these systems can often decay to one or more intermediate dark states or spectrally jump, resulting in the lack of photons on resonance. Here we present an optical co-excitation scheme that uses a weak nonresonant laser to reduce transitions to a dark state and amplify the photoluminescence from quantum emitters in hexagonal boron nitride (h-BN). Using a two-laser repumping scheme, we achieve optically stable resonance fluorescence of h-BN emitters and an overall increase of on time of an order of magnitude compared with only resonant excitation. Our results are important for the deployment of atomlike defects in h-BN as reliable building blocks for quantum-photonics applications.