We consider the analysis and design of space-time trellis codes (STTCs) for a cooperative relay channel operating in amplify-and-forward (AF) mode assuming the source and destination nodes are equipped with multiple antennas but the relay node has single antenna. We derive a pairwise error probability (PEP) expression for the performance of STTCs in this type of channels. A simple upper-bound on PEP is then derived and is maximized to find the optimum STTCs. We show that the designed STTCs based on the derived criterion achieve full diversity in the AF relay channels especially at high signal-to-noise-ratios (SNRs). The maximum achievable diversity in relay channels with single-antenna relay is bounded by $\min(M,N)$ where $M$ and $N$ are respectively the number of antennas in source and destination nodes. Simulation results confirm that the proposed codes achieve the maximum diversity and also provide an appealing coding gain.