We propose a coordinated multicell beamformer design method based on the signal-to-interference-plus-noise ratios (SINRs) balancing technique within the context of mixed quality of services (QoS). Instead of attaining an overall balance of SINRs to all users in all cells, the proposed algorithm allows a specific subset of users in each cells to achieve certain target SINRs while the SINRs of the remaining users in all cells are balanced subject to the total transmission power. The uplink-downlink duality is used for converting the downlink problem into the uplink beamformer design problem. The semidefinite programming (SDP) method is used to check the optimality.