Support fibers are commonly employed in microgravity droplet evaporation and combustion studies, and it is of interest to develop models of fiber-supported droplets. In this paper, a numerical study of the Marangoni forces on a methanol droplet supported by a fiber has been carried out for an evaporating methanol droplet in both dry air and humid air environments, with the focus being the development of instabilities that form early in the lifetime of a droplet. The thermal Marangoni effect has a stabilizing effect, and it is always driving the droplet surface toward an isothermal condition. The solutal Marangoni effect (from water absorption) is much larger in magnitude, and it tends to concentrate water on the surface. This tendency to concentrate water leads to surface waves and instabilities, which are relieved by diffusion of the water into the droplet interior. For large droplets (initial radii of 0.5 mm) the surface forces have generated liquid Reynolds numbers greater than one hundred. Smaller droplets (initial radii of 0.005 mm) give qualitatively similar results, however the Reynolds numbers are reduced by size and diffusion damping influences. The numerical simulations are sensitive to droplet and supporting fiber size, and it appears that experimental verification and comprehensive numerical studies should be fully three-dimensional. It also appears that the solutal Marangoni flows are unstable to very small wavelengths, as has been suggested by previous linearized stability analyses.