In this paper, we consider the weighted sum-rate (WSR) maximization problem in a cognitive relaying network under imperfect channel state information (CSI). The secondary network employs cooperative nonorthogonal multiple access (NOMA). We investigate the optimal power allocation and relay precoder design for the secondary network that shares spectrum with the primary network while keeping interference to the primary users below a threshold. We exploit the relation between the WSR and weighted mean-square error (WMSE) to solve the equivalent WSR maximization problem. We consider a practical scenario, where the available CSI of all the links are imperfect. The performance of the proposed solution is robust to the errors in the CSI. The optimization problem is intractable in its original form; however, we reformulate it as a tractable, equivalent optimization problem via certain transformations and approximations. We illustrate the robust performance of the proposed design via numerical simulation results.