The answer to this question is yes. Can you paint it any color you want? No. NFPA 58 states that propane containers must be painted a heat reflective color. Most state regulatory agencies have their own rule addressing this particular issue but the national code declares that LP Gas containers must be painted a heat reflective color unless installed in an extremely cold environment.
All too often propane customers take it upon themselves to paint their tank a color that complements the colors of their home or landscaping. This presents a safety problem as well as a serviceability problem if the tank color is dark or non-reflective. Dark colors absorb heat while lighter colors reflect it. Have you ever worn a dark colored shirt on a sunny day? A dark shirt on a sunny day will give you a lot more warmth than a white shirt will. The principle is the same with LP Gas tanks as the last thing any propane tank needs is to absorb heat. Perhaps a better example is walking barefoot on the concrete sidewalk and stepping onto the asphalt street on a hot sunny day. Concrete sidewalks are fairly light in color (heat reflective) while asphalt streets and roads ar dark in color (heat absorbent). The sidewalk is much more bearable to walk on while the asphalt road can be quite painful. Propane tanks need to reflect heat, not absorb it.
The entire reasoning behind propane tank color involves pressure and some simple laws of chemistry that apply to fluids and gases when they are heated. The law "as temperature increases, volume increases" applies and can be seen in this explanatory animation from NASA. Because propane exists as both a liquid and a gas within the tank, the absorption of heat due to a non-reflective color creates the possibility of a high pressure situation that may cause the safety relief valve to open. The bottom line is this:
Dark (Non Reflective) Propane Tank = Absorbed Heat = Propane Expansion = Relief Valve May Open
Below are actual photos of propane tanks that have excessive rust and are subject to over-pressure. In fact, rust is a color and will contribute to the absorption of heat. Rusted tanks pose another problem, pitting. Pitting occurs when a tank is excessively rusted and the surface of the tank is compromised. The rust will actually eat away at the surface of the tank. Tanks that are rusted often need to be sanded or scraped with a wire brush before they are painted.