The sketch window is always opaque so using get and getImage with it will never give you a transparent image.

Insted use createGraphics to create an offscreen image. The following code gives a simple demo - line 5 sets the background to fully transparent white.

1. void setup() {
2.   size(200, 200);
3.   pg = createGraphics(100, 100);
4.   pg.beginDraw();
5.   pg.background(color(255, 0));
6.   pg.stroke(255, 0, 0);
7.   pg.fill(255, 255, 0);
8.   pg.strokeWeight(10);
9.   pg.ellipse(pg.width*0.5, pg.height*0.5, 75, 75);
10.   pg.endDraw();
11.   image(pg, 50, 50);
12.   pg.save("test.png");
13. }

        pg.background(pg.color(255,0));

Change the way you create the image. How about...

1. PImage img = createImage(width, height, ARGB);

1. g= createGraphics(diameter+1, diameter+1);

Actually, you can hack your way to "force" the sketch's background itself to become transparent.
Then draw something in there, and crop it into a PImage/ Pgraphics later. 
And any unmodified pixels keep their transparency!

For further examples, go to post link below:
http://forum.processing.org/topic/shape-boudaries-for-mousepress

void setup() {
  size(300, 200);
  noLoop();
}

void draw() {
  color colour = color(#A0D0F0, 0200);
  loadPixels();

  for (int i = pixels.length; i != 0; pixels[--i] = colour);
  //for (int p: pixels)  p = colour;  // <-- Doesn't work. Dunno why!

  updatePixels();

  color pixel = get(width >> 1, height >> 1);
  println( hex(pixel) );
}