Despite the promising high-data rate features of visible light communications (VLC), they still suffer from unbalanced services due to blockages and channel fluctuation among users. This paper introduces and evaluates a new transmission scheme which adopts cooperative non-orthogonal multiple access (Co-NOMA) in hybrid VLC/radio-frequency (RF) systems, so as to improve both system sum-rate and fairness. Consider a network consisting of one VLC access point (AP) and multiple strong and weak users, where each weak user is paired with a strong user. Each weak user can be served either directly by the VLC AP, or via the strong user which converts light information received through the VLC link, and forwards the information to the weak user via the RF link. The paper then maximizes a network-wide weighted sum-rate, so as to jointly determine the strong-weak user-pairs, the serving link of each weak user (i.e., either direct VLC or hybrid VLC/RF), and the power of each user message, subject to user connectivity and transmit power constraints. The paper tackles such a mixed-integer non-convex optimization problem using an iterative approach. Simulations show that the proposed scheme significantly improves the VLC network performance (i.e., sum-rate and fairness) as compared to the conventional NOMA scheme.