The dark rays in the atmosphere are caused by shadows cast from the clouds. The point where all the rays converge to one point is where you are looking directly away from the sun. Since you are not rendering the planet's surface, you are looking very deep into the atmosphere, something none of us have ever seen in real life because the ground is never more than a few kilometres below us, so it looks a bit strange when we can see so deep into the atmosphere, but not necessarily wrong. (But I guess if you could see this in real life there probably would be more scattering which would make these deep rays less prominent.)
The really dark rays are below the horizon. The first question I would ask is whether they will even be visible inside the game or environment where this skybox will be used. Even up to a few degrees below the horizon your rays are not excessively dark - it is only when you look much lower that they seem too strong.
You can reduce the contrast of the rays by adding more environment/ambient light to the atmosphere. Either one of the following will work: Increasing the "strength in atmosphere" setting on the Enviro Light node, or increasing the "Ambient" setting in the Atmosphere node. Doing this will weaken the rays where you probably do want them though. The rays above the horizon seem nice and natural, and if it were me I would not want to diminish those.
EDIT: Make sure that your render settings have both "GI relative detail" and "GI sample quality" at 1 or higher, otherwise your Enviro Light will have no effect. The Enviro Light is needed to lighten the shadows by accounting for scattered light.
Enabling soft shadows on the sunlight might help to soften the rays a little bit. It might keep the rays where you want them but diminish them over longer distances. But be aware that soft shadows will probably increase noise which you would need to compensate for with higher number of samples in the sunlight node or in the atmosphere node (or both).
Matt
