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Probably not easy to impliment yet, but scientists have discovered that just as colored paints reflect certain wavelengths of light and reflect others, one that reflects visible and ultraviolet light, yet is dark and absortive in the infrared spectrum, can maintain a temperature below ambient air temperatures by several degrees. Add a dark roof, perhaps no liner at all, just this material on the roof, and you have an interior passive cooling system.
The way it works is that the hotter something is, the higher the wavelenghts it gives off (get something hot and it starts to glow in the visible spectrum, first red, then yellow, then eventually blue or even violet until it starts producing ultraviolet). At around ambient temperatures, however things usually give off infrared radiation, which cools it. The problem is that this mainly applies to non-reflective surfaces (infrared guns have a hard or impossible time telling the temperature of a reflective surface). But the dilema is that by making something non-reflective in infrared, it usually gives off infrared, but if it's also non-reflective in visible and ultraviolet light, it then absorbs those. And if it's reflective in visible and ultraviolet, like your "cool white roof" it also will not shed heat in infrared. So the key is to make it non-reflective and dark in infrared, but reflective or white in visible and ultraviolet.
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