The paper considers a wireless network in which simultaneous communications occur within multiple single antenna source-destination node pairs. An Amplify-and-Forward (AF) relay, equipped with multiple antennas, assists the communication. The relay implements linear beamforming (BF) aiming to minimize the total relay power subject to signal-to-interference ratio (SINR) constraints for each source-destination (S-D) pair. A relay transmission scheme is proposed that instead of assuming the availability of full channel state information (CSI), a typical assumption in such scenario, it considers a more practical case in which there is CSI error at the relay. The maximum SINR loss due to the imperfect CSI is computed and used to further tighten the SINR constraints of each S-D pair. A method recently proposed by the authors  is then used along with the tighter SINR constraints to obtain the beamforming weights. The proposed approach is computationally simple and simulation results show that it greatly reduces outage probability.