No you simply can't change the color of an image in Titanium. If you want to achieve your goal i would simplify the shape for example take a circle. To draw a circle use this code:
var circle = Ti.UI.createImageView({
width: 100,
height: 100,
borderRadius: 50,
backgroundColor: 'black'
});
To change it's color use this event listener:
circle.addEventListener("click", function(e){
circle.backgroundColor = "red";
});
This will only change the color to red on the first click. If you want to randomize the colors you'll have to create an array with colors in it. Then use a shuffle function to get a random color to eventually set it. This article might be helpfull: shuffle
Good luck!