In this paper, we analyze the outage probability of multiple-input multiple-output cognitive cooperative radio networks (CCRNs) with multiple opportunistic amplify-and-forward relays. The CCRN applies underlay spectrum access accounting for the interference power constraint of a primary network and utilizes orthogonal space-time block coding to transmit multiple data streams across a number of antennas over several time slots. As such, the system exploits both time and space diversity to improve the transmission reliability over Nakagami.. fading. The CCRN applies opportunistic relaying in which the relay offering the highest signal-to-noise ratio at the receiver is selected to forward the transmit signal. Furthermore, selection combining is adopted at the secondary receiver to process the signal from the direct and relaying transmissions. To evaluate system performance, we derive an expression for the outage probability which is valid for an arbitrary number of antennas at the source, relays, and receiver of the CCRN. Selected numerical results are provided using Mathematica for analysis and Matlab for simulations, to reveal the effect of network parameters on the outage probability of the system.