An adaptive delay-tolerant distributed space-time coding (DSTC) scheme with feedback is proposed for two-hop cooperative multiple-input multiple-output (MIMO) networks using an amplify-and-forward strategy and opportunistic relaying algorithms. Maximum likelihood receivers and adjustable code matrices are considered subject to a power constraint. In the proposed delay-tolerant DSTC scheme, an adjustable code matrix is employed to transform the space-time coded matrices at the relay nodes. Stochastic gradient algorithms are developed with reduced computational complexity to estimate the parameters of the code matrix. Simulation results show that the proposed algorithms obtain significant performance gains and address the delay issue in cooperative MIMO systems as compared to existing DSTC schemes.