In a typical toilet, the water in the bowl is the trap that prevents sewer gasses from getting into the house. If you don't replace the toilets with something that is designed to do that function while dry then you must keep the water in the bowl. Vegetable oil would dry up and gunk on the sides. Mineral oil would be less prone to this. And on a strange note, swimming pool supply houses have an odd liquid product (in some floating thing) that claims to keep a pool warmer. It does this by forming a molecule thick layer on top of the water that prevents evaporation. If you stop the evaporation, you keep the water in the bowl without the ring (due to minerals solidifying during evap). I return you to your regularly scheduled programming.
Or just go flush them on occasion as has been mentioned.