Non-orthogonal multiple access (NOMA) has recently been proposed as a key enabling technology for the fifth generation (5G) wireless networks. Different from the existing works which focus on the performance analysis of NOMA with backlogged traffic, in this paper, we analyze the stable throughput region of downlink NOMA transmission with dynamic traffic arrival for users with different priorities. By utilizing limited instantaneous channel state information (CSI) at the base station, we propose an opportunistic NOMA scheme to enhance the network performance. Considering both NOMA and dynamic traffic arrival leads to interacting queues, which complicate the performance analysis. By using tools from stochastic geometry and queueing theory, we decouple the interacting queues and characterize the stable throughput region of the proposed opportunistic NOMA scheme in terms of the threshold to trigger NOMA and transmission power allocation coefficients. Numerical results show that, compared to the orthogonal multiple access scheme, the proposed opportunistic NOMA scheme can significantly enhance the stable throughput region when the design parameters are appropriately selected.