This paper considers cognitive multiuser two-way relay networks (MU-TRNs) where multiple secondary users (SUs) concurrently exchange their data with other SUs with an aid of a two-way relay in licensed primary networks. In this paper, we particularly focus on linear relay filter designs that effectively minimize the mean square error of SUs while providing a certain level of quality of service for the primary network. To this end, we first propose an iterative algorithm that identifies a solution based on an alternating optimization technique. Then, a closed-form relay filter design is presented, which employs a high signal-to-noise ratio approximation to reduce the computational complexity. Through the simulation results, we confirm that the proposed closed-form relay filter design outperforms conventional approaches and provides the performance close to the proposed iterative algorithm with much reduced complexity.