Reds...indeed they are difficult on most any brand of camera. I've had some luck too by lowering exposure, tinkering with WB, and decreasing saturation.....
as mentioned by Anders.
Lowering exposure is the most useful for me. Still, there are so many shades of red that no single setting will reproduce all the shades you run across.
Worked here, but that is not always the case.
I spent a day once looking at galleries of Cardinals by various brands of cameras.....Canon seemed to be the worst at that time, and Nikon and Pentax were about the same. Few did a consistently good job, in fact, I don't recall any that did judging by what I saw.
This one is pretty close too, but the bird has a little more orange tint in nature, so it was a little harder to process.
In the case of Cardinals, and roses, few are of the same tint.
Then you get to Woodpeckers and it's a whole 'nother problem!
Also...try setting WB to flash, without using flash...sometimes it will give you a true red.
Regards!