The cooperative relay network is a type of multi-terminal communication system. We present in this paper a Neural Network (NN)-based autoencoder (AE) approach to optimize its design. This approach implements a classical three-node cooperative system as one AE model, and uses a two-stage scheme to train this model and minimize the designed losses. We demonstrate that this approach shows performance close to the best baseline in decode-and-forward (DF), and outperforms the best baseline in amplify-and-forward (AF), over a wide range of signal-to-noise-ratio (SNR) values. It is also shown that training at a list of mixed SNR values can improve the error performance compared to training at a fixed SNR value. Moreover, to verify the robustness of the trained AE model, we test it under the effect of impulse-noise.