This paper considers the downlink of a cognitive radio (CR) network formed by multiple primary and secondary transmitters, where each multi-antenna transmitter serves a pre-known set of single-antenna users. The paper assumes that the secondary and primary transmitters can transmit simultaneously their data over the same frequency bands, so as to achieve a high system spectrum efficiency. The paper considers the downlink balancing problem of maximizing the minimum signal-to-interference-plus noise ratio (SINR) of the secondary transmitters subject to both total power constraint of the secondary transmitters, and maximum interference constraint at each primary user due to secondary transmissions. The paper proposes solving the problem using the alternating direction method of multipliers (ADMM), which leads to a distributed implementation through limited information exchange across the coupled secondary transmitters. The paper additionally proposes a solution that guarantees feasibility at each iteration. Simulation results demonstrate that the proposed solution converges to the centralized solution in a reasonable number of iterations.