We consider a two-user multi-relay cooperative non-orthogonal multiple access (NOMA) network with distributed space-time coding. Two dual-relay selection strategies are proposed for cooperative NOMA, namely, two-stage dual relay selection with fixed power allocation (DRS-FPA) and two-stage dual relay selection with dynamic power allocation (DRS-DPA). Furthermore, lower and upper bounds on the outage probability for the DRS-FPA scheme and the exact outage probability for the DRS-DPA scheme are obtained in closed-form, respectively. Numerical results show that the proposed two-stage DRS schemes not only yield better outage performance than the existing single relay selection schemes without sacrificing spectral efficiency, but can also achieve full diversity gain.