The development of relay transmissions have recently attracted increasing interests in wireless communications since they provide cooperative diversity gains by forming virtual antenna arrays. In such relay networks, optimum energy allocation is critical to enhance their performance and efficiency. However, existing works on performance analysis and optimization mainly focus on single-relay systems. In this paper, an upper bound of the error performance is derived with arbitrary number of relays. Based on this bound, we then develop the optimum energy allocation schemes that minimize the average system error. Equally attractive is that our investigation is tailored for differential modulations, which bypass the channel estimation at the receiver and are particularly suitable for wireless relay networks. The performance improvement of the optimized systems over the un-optimized ones is confirmed by analytical and simulated comparisons.