Reconfigurable intelligent surfaces (RISs) become promising for enhancing non-orthogonal multiple access (NOMA) systems, i.e., enhancing the channel quality and altering the SIC orders. Invoked by stochastic geometry methods, we investigate the downlink coverage performance of RIS-aided multi-cell NOMA networks. We first derive the RIS-aided channel model, concluding the direct and reflecting links. The analytical results demonstrate that the RIS-aided channel model can be closely modeled as a Gamma distribution. Additionally, interference from other cells is analyzed. Lastly, we derive closed-form coverage probability expressions for the paired NOMA users. Numerical results indicate that 1) although the interference from other cells is enhanced via the RISs, the performance of the RIS-aided user still enhances since the channel quality is strengthened more obviously; and 2) the SIC order can be altered by employing the RISs since the RISs improve the channel quality of the aided user.