Filling of carbon single-wall nanotubes (SWNTs), of diameter d = 11.5-15 Å, by silver iodide from the melt is modeled by molecular dynamics. Formation of AgI inorganic nanotube (INT) structures in the SWNTs on cooling, and ion diffusion in AgI within the tubes (AgI@SWNT) at 500-1200 K are studied. Dependence of AgI@SWNT structure on carbon SWNT geometry is examined. For d ≤ 14.2 Å, a single-wall AgI INT is formed within the carbon tube, with structure (geometry) depending on d; in wider tubes, there are extra silver and iodine ions in the central region. The calculated diffusion coefficients of silver and iodine ions and their diffusion activation energies depend on the nanotube geometry. Ion mobilities within carbon SWNTs are significantly lower, and diffusion activation energies, higher than in the bulk phase of AgI, especially in narrow tubes. In the (11,11) carbon SWNT, the widest among those simulated, the activation energy for silver ion diffusion becomes close to the "bulk" value, while for iodine ions, larger in size, the difference remains.