Semiclassical approximations to response functions can provide quantum mechanical effects for linear and nonlinear spectroscopic observables to be calculated from only classical trajectories as input. The two major components needed to evaluate a response function are the thermal weights for the system's initial conditions, and the calculation of the dynamics from those conditions. One such class of approximations for vibrational response functions utilizes classical trajectories at quantized values of classical action variables, with the effects of the radiation-matter interaction represented by discontinuous transitions. An alternative weight to the classical distribution is investigated and attempts to incorporate this both with and without this quantized action approach are presented. Two forms are constructed that yield the correct linear response function for a harmonic potential at any temperature and are also correct for anharmonic potentials in the classical mechanical limit of high temperature. Approximations to the vibrational linear response function with quantized classical trajectories and proposed thermal weight functions are assessed for ensembles of one-dimensional and coupled anharmonic oscillators. This approach is shown to perform well for an anharmonic potential that is not locally harmonic over a temperature range encompassing the quantum limit of a twolevel system and the limit of classical dynamics.