Here' s a few thoughts. The speakers you now have could be underpowered by the stock headunit especially if the previous owner decided to upgrade to better and more power hungry speakers. If this is the case, much of the "rattle" is probably speaker distortions.....Solution could be as simple as returning to the OEM speakers or something just as effecient or even better adding a small amp to power your present speakers.
If distortion is NOT the problem, follow the previous recs and track down the parts that may be vibrating inside the door panel. You can also experiment with sound deadning materials like Dynamat. Don't give up, the problem can be solved. Good luck