We introduce a coarse-grained approach for characterizing the long-timescale dynamics of ion diffusion in general polymer electrolytes using input from short molecular dynamics trajectories. The approach includes aspects of the dynamic bond percolation model [J. Chem. Phys. 1983, 79, 3133-3142] by treating ion diffusion in terms of hopping transitions on a fluctuating lattice. We extend this well-known approach by using short (i.e., 10 ns) molecular dynamics (MD) trajectories to predict the distribution of ion solvation sites that comprise the lattice and to predict the rate of hopping among the lattice sites. This yields a chemically specific dynamic bond percolation (CS-DBP) model that enables the description of long-timescale ion diffusion in polymer electrolytes at a computational cost that makes feasible the screening of candidate materials. We employ the new model to characterize lithium-ion diffusion properties in six polyethers that differ by oxygen content and backbone stiffness: poly(trimethylene oxide), poly(ethylene oxide-alt-trimethylene oxide), poly(ethylene oxide), poly(propylene oxide), poly(ethylene oxide-alt-methylene oxide), and poly(methylene oxide). Good agreement is observed between the predictions of the CS-DBP model and long-timescale atomistic MD simulations, thus providing validation of the model. Among the most striking results from this analysis is the unexpectedly good lithium-ion diffusivity of poly(trimethylene oxide-alt-ethylene oxide) by comparison to poly(ethylene oxide), which is widely used. Additionally, the model straightforwardly reveals a range of polymer features that lead to low lithium-ion diffusivity, including the competing effects of the density of solvation sites and polymer stiffness. These results illustrate the potential of the CS-DBP model to screen polymer electrolytes on the basis of ion diffusivity and to identify important design criteria.