We consider a cognitive radio (CR) scenario where the signals transmitted by a secondary user are relayed using an amplify-and-forward cooperation protocol. A distributed strategy for power allocation is derived that minimizes the outage probability of the cooperative CR communication system, under the constraint that the interference power experienced by the primary receiver does not exceed a given threshold. First, assuming that each CR node has ideal channel state information about its interference channel, we show that the average interference power constraint gives better outage probability performance than the peak power constraint. Then, when only channel statistics are available for the interference channel, the outage probability is verified to lie in between the results relevant to the average and peak power constraints, respectively, with ideal channel state information.