In this work, the issue of joint relay selection and power allocation in Underlay MIMO Cooperative Cognitive Radio Networks (U-MIMO-CCRN) is addressed. The system consists of a number of secondary users (SUs) in the secondary network and a primary user (PU) in the primary network. We consider the communications in the link between two selected SUs, referred to as the desired link which is enhanced using the cooperation of one of the existing SUs. The core aim of this work is to maximize the achievable data rate in the desired link, using the cooperation of one of the SUs which is chosen opportunistically out of existing SUs. Meanwhile, the interference due to the secondary transmission on the PU should not exceed the tolerable amount. The approach to determine the optimal power allocation, i.e. the optimal transmits covariance and amplification matrices of the SUs, and also the optimal cooperating SU is proposed. Since the proposed optimal approach is a highly complex method, a low complexity approach is further proposed and its performance is evaluated using simulations. The simulation results reveal that the performance loss due to the low complexity approach is only about 14%, while the complexity of the algorithm is greatly reduced.