A simple reason the sky isn’t green is that the sun is not orange. The sun’s color relates to its surface temperature via something called black body radiation. That is, if you heat up a black object it will first glow red, then orange, yellow, green etc. In each case glowing in a color that represents its temperature. Our star is called a yellow sun; this is to say that the center of the radiation in our sun provides is yellow, while the majority of the spectrum is from violet to red. The sun also radiates some energy as invisible light, ultraviolet and infra-red, but not all that much.

Thus, in case you want to know why the sun isn’t blue or green, it’s that the sun is too cool to be these colors.

Of the light of the sun, some small amount (about 10%) scatters off of the molecules int he air. This is called Rayleigh scatter, and the fraction radiated is proportional to the 4th power of the frequency. Because the scatter is frequency dependent, the high frequencies (blue, indigo, and violet) scatter a lot, about 20%, while the red hardly scatters at all. As a result the sky looks blue, while the sun looks pretty much the same if viewed from earth or from space

The sun looks orange at sundown because the sunlight has to go through more air, and a lot more of the yellow, green, and blue scatter away before we see it. I might expect the sky to look somewhat greenish at sundown, but I have not noticed. If the molecules in the air were bigger we’d still see the same color, though its intensity would be greater. That’s the effect that carbon dioxide has — it causes more sunlight to scatter, making the sky a brighter blue (it also holds in the infra-red, but that’s a different story). If the sun were cooler (orange say), the sky might appear as green. That’s because there would be less violet and blue in the sunlight, and the sky color would be shifted to the longer wavelengths. My summary is thus, that on planets where the sun is cooler than ours, the sky is green.