Visible light communication (VLC) is a promising communication technology that benefits from several advantages over other wireless communication techniques. However, the capacity of VLC systems is limited by the low modulation bandwidth of light-emitting diodes (LEDs) used as transmitters. To circumvent this bottleneck, non-orthogonal multiple access (NOMA) is popularly used in VLC systems. However, due to high inter-user interference at the receivers, NOMA suffers from poor outage performance, especially if the number of users is large. We propose to boost the outage performance of a NOMA-based VLC system by incorporating multi-user cooperative diversity over radio frequency (RF) links, thereby transforming it into a hybrid VLC-RF system. Such a system with cooperative NOMA (CoNOMA) has enhanced reliability compared to a conventional non-cooperative NOMA system. We formulate the expressions for the outage probability of the proposed system and analyze the outage performance for various power allocation schemes used in NOMA. We study the effects of increasing the number of users and the target data rate on the system’s overall outage performance. We also model the reliability of the multi-user CoNOMA system using Markov chains and evaluate the various reliability parameters for each user. We show that the outage performance and reliability of the VLC system are significantly enhanced by employing cooperative diversity using CoNOMA.