This paper investigates the performance of a new framework for low-outage downlink non-orthogonal multiple access (NOMA) using a coordinated direct and relay transmission (CDRT) scheme with direct links to both the near-user (NU) and the far-user (FU). Both amplify-and-forward and decode-and-forward relays are considered. In this framework, the NU combines the signals from base-station and relay at each stage of the successive interference cancellation (SIC) to attain good outage performance. For both NU and FU, the expressions for outage probability and throughput are derived in closed form. We also derive the high-SNR expressions for the outage probability to demonstrate that with the proposed framework, both users harness a diversity of two without feedback bits (this is the only framework to achieve this). We demonstrate that the choice of power allocation coefficient and target symbol rates is crucial to maximizing the NU throughput while ensuring a desired target FU throughput. We demonstrate that CDRT with the proposed framework outperforms known schemes in terms of outage probability, sum throughput, and energy efficiency. Moreover, we also show that optimal rate selection is important to maximize the energy efficiency. Monte Carlo simulations validate the accuracy of the derived analytical expressions.