This paper presents a novel deep joint source-channel coding (DeepJSCC) scheme for image transmission over a half-duplex cooperative relay channel. Specifically, we apply DeepJSCC to two basic modes of cooperative communications, namely amplify-and-forward (AF) and decode-and-forward (DF). In DeepJSCC-AF, the relay simply amplifies and forwards its received signal. In DeepJSCC-DF, on the other hand, the relay first reconstructs the transmitted image and then re-encodes it before forwarding. Considering the excessive computation overhead of DeepJSCC-DF for recovering the image at the relay, we propose an alternative scheme, called DeepJSCC-PF, in which the relay processes and forwards its received signal without necessarily recovering the image. Simulation results show that the proposed DeepJSCC-AF, DF, and PF schemes are superior to the digital baselines with BPG compression with polar codes and provide a graceful performance degradation with deteriorating channel quality. Further investigation shows that the PSNR gain of DeepJSCC-DF/PF over DeepJSCC-AF improves as the channel condition between the source and relay improves. Moreover, the DeepJSCC-PF scheme achieves similar performance to DeepJSCC-DF with lower computational complexity.