Click the mouse anywhere in the "word area" (the area in which correctly guessed letters appear) to cycle through all the possible color choices. Press the shift key before clicking to cycle backwards through the same color choices.
Click the mouse anywhere in the background of the large guessing letters to similarly cycle through all possible colors for this area of the game. As above, press the shift key before clicking to cycle backwards through the same color choices.
Your color preferences will be saved automatically.