Bizncs“Rain is falling down”
Not good.
Bizncs“Rain is coming”
Not good at all. But in a slightly different meaning:
It looks like rain is coming soon. (The sky is dark; the wind is blowing. It is not yet raining.)
Bizncs“Rain is coming down”
Better with a modifier, thus:
The rain is really coming down! -- to indicate a very intense rain. Not good for a simple statement that it's raining.
CJ