Coffee stains in the carpet can be removed and this video shows some good techniques for removing coffee from carpet, with some notable exceptions. First, I'm a professional carpet cleaner in Tampa FL and have years of experience in removing all types of carpet stains. It's important to remove stains without damaging your carpet. If you use bleach on your carpet the manufacturer's warranty could be voided.
Instead of using bleach to get coffee stains out of carpet I would use vinegar and a very small amount of dish soap in very hot water. The soap and vinegar will not put the carpet at risk and will give you the same results as seen on the video.
The steam iron does a great job of bringing the coffee to the surface and into the towel. The mechanical lifting of the steam is what is removing the stain more so than the solution.
If you live in Tampa FL and have a tough coffee stain call Chem-Dry of Tampa FL for professional stain removal.