In this paper, we investigate the Power Allocation (PA) problem for Cooperative Orthogonal Frequency Division Multiplexing (C-OFDM) communication system with a relay which Decodes and Forwards (DF) the data and with Binary Differential Phase Shift Keying (BDPSK) modulation. We propose the optimal power allocation algorithms to minimize Average Bit Error Rate (ABER). In the optimal algorithms, the system firstly allocates power for each sub-carrier pair, and then allocates power in every sub-carrier pair. In addition, the performance of optimal scheme with simple sub-carrier pairing proposed in this paper is better. Simulation results show that significant performance gains can be achieved by the proposed algorithms.