In this paper, we examine a full-duplex transmission scheme for cognitive cooperative radio networks (CCRNs) to improve capacity. In this network, the secondary transmitter and secondary relay are allowed to utilize the licensed spectrum of the primary user by using underlay spectrum access. We assume that the CCRN is subject to the interference power constraint of the primary receiver and maximum transmit power limit of the secondary transmitter and secondary relay. Under these constraints, we propose an optimal power allocation policy for the secondary transmitter and the secondary relay based on average channel state information (CSI) to optimize capacity. Then, we derive an expression for the corresponding achievable capacity of the secondary network over Nakagami-m fading. Numerical results are provided for several scenarios to study the achievable capacity that can be offered by this full-duplex underlay CCRN using the proposed optimal power allocation scheme.