The vibrational dynamics of a model diatomic anion solute dissolved in a methyl iodide solvent confined in a nanoscale spherical cavity are investigated by molecular dynamics simulations. The effect of confining the solvent on the vibrational energy relaxation time T-1, solvent-induced frequency shift , and pure dephasing time T-2* is examined by comparing the results from confined systems of varying size (cavity radius 0.8-2 nm) to those from the bulk system. It is found that T-1 increases monotonically toward the bulk solvent value with increasing cavity size, and good agreement is found between equilibrium molecular dynamics simulations based on perturbation theory and classical nonequilibrium dynamics simulations. In contrast to T-1, the solvent-induced frequency shift and the dephasing time do not change monotonically with cavity size. The results are discussed in terms of the changes in solvent structure and dynamics due to confinement.