This paper presents a joint subcarrier and power allocation algorithm for cooperative multiuser orthogonal frequency division multiplexing (MU-OFDM) cognitive radio (CR) systems. By simplifying a three-node relay network to a two-node network with the equivalent channel gain, we formulate the resource allocation problem for a cooperative MU-OFDM CR system in a similar form to that for a non-cooperative MU-OFDM CR system. With this problem formulation, a rule is derived for performing subcarrier assignment operations under a given power distribution, where the sum capacity optimization is alternated between the subcarrier and power to form a joint subcarrier and power allocation algorithm. To simplify the high-complexity optimal power allocation algorithm (i.e., the iterative partitioned water-filling algorithm) for the joint scheme, we further develop a simple method for updating the water level when each subcarrier is assigned. Simulation results show that, with or without cooperative transmission, using the proposed method to update the water level achieves a system capacity close to that of the joint subcarrier and power allocation algorithm with the optimal power distribution. In addition, if the relay node is at the midpoint between the source and destination, the system capacity can reach its maximum value.