By saving the color you're drawing. So you'll only randomly generate it once, and then keep using that color to redraw each time.
Either generate it before the draw like Color c = new Color(randomNum.nextInt(256), randomNum.nextInt(256), randomNum.nextInt(256));
or only generate the variable and test if it has been initialized in your draw method. If it hasn't (the first time running your code), you generate a random color, if it has been initialized, you just skip generating the color and go straight to your g.fillOval