In this work, we study an end-to-end deep learning (DL) based constellation design for the amplify-and-forward (AF) relaying network. Firstly, we study the one-way (OW) and two-way (TW) AF relay networks as an autoencoder by utilizing a single channel to transmit the desired bits, whilst operating under Rayleigh fading channels. As a result of optimal constellation design via end-to-end DL-based framework, we achieve a performance gain of 4 dB and 1.2 dB at 10 dB average signal-to-noise ratio (SNR) over conventional OWAF and TWAF relay networks, respectively. Secondly, by adding redundant bits at the transmitter, we jointly design an end-to-end DL-based coding and modulation scheme for block fading Rayleigh channels. This leads to DL-based coding and modulation, and DL-based differential coding and modulation, similar to the coded modulation and differential coded modulation in conventional networks, depending upon the presence of channel state information knowledge at the receivers. Thus, we propose an end-to-end DL-based data-driven frameworks for differential coded modulation in OWAF and coded modulation in TWAF relay networks. Lastly, we show that at 20 dB average SNR, our proposed methods (DL based differential coded modulated OWAF and DL-based coded modulated TWAF) achieve a gain of 4 dB and 4.8 dB, over conventional OWAF and TWAF relay networks employing Hamming codes with same rates.