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We present a novel implementation of an adaptive generalized sidelobe canceller beamformer, using a coupled nonlinear oscillator array in conjunction with an antenna array. This beamformer is applied in a narrowband wireless communication context, where there is contamination due to transmissions from similar systems. We have applied a least mean square like algorithm to compute weight updates so as to reject the interfering signals while maintaining the desired beam. The actual update of the beamformer weights is performed indirectly, via adjustment of the coupling parameters of the coupled nonlinear oscillator array. Computer simulations of the proposed approach are presented for a narrowband communication system. The simulation results show successful adaptation towards the rejection of the interfering communication signals.