The first step is to figure out where the noise if coming from. I would remove the e-clip and the square actuator from the bottom of the stick so no switches can be hit and see if it still makes the noise. If so, it's likely the internal spring.
Pull the whole thing apart and shoot some silicone spray inside the spring cavity. Make sure you get a good shot everywhere the spring makes contact with the plastic, as well at the parts where the spring coils back on itself. I'm guessing you won't have any creaking after that.
RandyT