I’m confused; wouldn’t you want it to reflect the solar radiation, not absorb it? The energy has to go somewhere! Unless the energy is going into something else, like increasing some chemical potential energy, or producing electrical power, or something, if it is absorbed, it is as heat. While, if it is reflected, (some proportion of) it may leave the earth as light.

I guess something which might help is if you could change the wavelengths that went out from it to be ones that would be more likely to leave earth rather than being absorbed/reflected by the atmosphere? But I don’t know if that can be done efficiently enough to not produce more heat in the process of changing the wavelengths than just reflecting it would, if it is even possible.