Reliability is significant for unmanned aerial vehicle (UAV)-assisted air-to-ground (A2G) communications. In this letter, we address the reliability optimization problem by properly scheduling data transmissions under Non-Line-of-Sight (NLoS) channel fading. We capture the channel fading effect by the Rayleigh distribution and then formulate the A2G communication reliability from a probabilistic perspective. We propose a constrained optimization model that jointly takes into account the impacts of the aerial and ground nodes' mobility, the stochastic fading characteristics of the A2G channel, and the transmission constraints. From the model, we derive a closed-form reliability-optimal solution for data transmission scheduling and theoretically characterize the optimal reliability that is achievable. Simulation results verify our theoretical results and show the superior performance of the proposed scheduling solution over benchmark methods.