Technically you could do it by changing the back color
of the form in question into "public" and then changing
that color from elsewhere in the system, like you would
change any other value (assuming you are doing that
directly - i.e., without a get / set operation, which some
would say is bad practice).
However, my experience is that if you try to change the color
of a form from elsewhere in the system Visual C#.Net gets into
a mess.
I tried to do it once, because I wanted to give the user of
the system the option of changing screen colors etc. to his
personal liking. But Visual Studio started protesting.
If you find a way out let me know.