A good epoxy will work but there might be some longer term adhesion issues. You will need to do a very good cleaning first to remove any soap scum, mold or whatever might be on the surface. A light sanding on smooth surfaces using 220 or finer sandpaper is recommended. Plus an epoxy primer is also a good idea.
There's appliance/tub painting kits on the market. One of these will be a good choice.