I shoot with a Nikon DSLR, so others might be better suited to give advise here, but it seems your camera has a lot of weird settings for color. Wouldn't be surprised if some of these are affecting your results.
My suggestion after reading the manual a bit would be to try this:
I would select the P mode of your camera(page 57 in your manual)
Change the image color tones (My Colors) (page 60 and 61) to either "Neutral" or "My Colors Off".
If that isn't satisfactory go to Custom Color (Page 61) and adjust these settings manually to taste.
If needed you can adjust the white balance to either cloudy or daylight as suitable (Page 60). Later on you might want to use a custom white balance.
So in conclusion you can adjust almost every aspect of color in camera, so with some tweaking (white balance might need adjustment on a shoot by shoot basis if the light changes) you should be able to get the colors you want.
