In this paper, we study the resource allocation problem for a single-cell non-orthogonal multiple access (NOMA) relay network where an OFDM amplify-and-forward (AF) relay allocates the spectrum and power resources to the source-destination (SD) pairs. We aim to optimize the resource allocation to maximize the average sum-rate. The optimal approach requires an exhaustive search, leading to an NP-hard problem. To solve this problem, we propose two efficient many-to-many two-sided SD pair-subchannel matching algorithms in which the SD pairs and sub-channels are considered as two sets of players chasing their own interests. The proposed algorithms can provide a sub-optimal solution to this resource allocation problem in affordable time. Both the static matching algorithm and dynamic matching algorithm converge to a pair-wise stable matching after a limited number of iterations. Simulation results show that the capacity of both proposed algorithms in the NOMA scheme significantly outperforms the conventional orthogonal multiple access scheme. The proposed matching algorithms in NOMA scheme also achieve a better user-fairness performance than the conventional orthogonal multiple access.