In this paper, for an overlay cognitive radio system in which the primary users' information exchange is assisted by a secondary multiple-input multiple-output two-way relay network, we propose two spectrum sharing schemes that achieve the full diversity gain in both the primary and secondary networks. In the spectrum sharing problem that we formulate, there are two degrees of freedom to be optimized: relay selection and spectrum allocation. We jointly optimize these two degrees of freedom such that the achievable rate in the secondary network is maximized under the constraint that a minimum quality of service requirement in terms of the achievable rate is satisfied for the primary network. We analyze the performance of the proposed schemes in terms of the outage probability (that reflects the rate of unsuccessful spectrum sharing), the asymptotic behavior and the diversity order over Rayleigh fading channel. The analysis of the paper shows that in both of the proposed schemes, the full diversity of order NM² is achieved by the primary users, where N is the number of the secondary users and M is the number of antennas per terminal. Moreover, in both of the schemes, the full selection diversity of order NM² is guaranteed for the secondary network. We also provide extensive simulation results to confirm the theoretical analysis of this paper.