This study presents a two-stage power allocation for the amplify-and-forward (AF) cooperative networks with distributed generalised ABBA (GABBA) space-time codes. The new power allocation scheme first determines the transmit power between the source node and the relay nodes by maximising the instantaneous rate, and thereafter optimises the power distribution among the relay nodes via the water-filling. Also, a maximum-likelihood detection, which makes use of the encoding structure of the distributed GABBA space-time codes, is addressed to alleviate the computational overhead. Moreover, a performance analysis including the array gain and the diversity gain is also scrutinised to provide further insights into the cooperative networks considered, where the destination is equipped with multiple antennas. Conducted simulations show that the GABBA coded AF cooperative networks incorporated with the proposed two-stage power allocation can attain close or even superior performance compared with previous works but with substantially reduced computational complexity.