This paper investigates a centralized cooperative cognitive radio network (CCRN) where a primary base station (PBS) transmits a message to a primary user while a secondary user transmitter (SU-Tx) function as a friendly jammer. The jammer sends jamming signals to protect the PBS’s messages from a potential eavesdropper (Eve). However, the SU-Tx also attempts to covertly transmit its own messages to a secondary user receiver using the allocated spectrum resource, contravening the PBS regulations. To address this issue, the PBS requests its partner CBS to help detect jammer’s behavior. Specifically, we propose a generative adversarial network (GAN) optimization framework that models the strategic game between the CBS monitoring and the covert transmission of cooperative jammers. We introduce a novel GAN-based beamforming design algorithm, termed GAN-BD, to determine the power allocation at the jammer for covert communication. Additionally, we develop the detection error probability (DEP) at the CBS and derive its expression using a hypothesis testing problem. Through extensive simulation results, we demonstrate that the proposed GAN-BD algorithm can achieve near-optimal solutions for conducting covert communication, leveraging knowledge of the current network environment and exhibiting rapid convergence capabilities. The simulation results highlight the effectiveness of our GAN-BD algorithm.