The sun acts like a black body radiator at about $T=6000K$. Thus, its "natural" color is the superposition of all colours, which we experience as white. The "red" color, which we experience during sun rise and sun set are effects due to Rayleigh scattering, which is wavelength dependent, $\sigma \propto 1/\lambda^4$. This explains two well-known phenomena:
- If the sun is just above the horizon there is "a lot" of atmosphere between the emitter (=sun) and the observer (=us). Hence, the "short" wavelengths components of the sun light have been scattered and the observers detects only the non-scattered photons. These are mostly red.
- During the day, if the sun is over our head, the observer detects only those photons, which are scattered. As these are predominantly the "short" wavelength components the sky appears blue.
As green is in the center of the visible spectrum it is almost impossible to get the correct amount of scattering for a green sky. However, there is the so called green flash -- I linked some pictures -- just after the sunset. I have been told that this is not a scattering effect, but a refraction effect. Although this makes sense to me, I let the experts here explain it in greater detail.