Depending on what color you'd like to reach, I remember taking a trip into Arizona around Sedona & Phoenix. They had Red Rock shirts that had allegedly been dyed with dust from the area and they were a darker reddish brownish color.
Search for red dirt shirt or sedona red dirt dyed shirt you should come up with a link for what the color looks like. If I remember correctly that's the color I recall them being.
The dirt/sediment from that area will stain/dye just about anything. I had to replace some clothes after coming back from that trip. If you like that coloring, I would imagine one would get ahold of some of that dirt, place it in a bucket with water and the chosen item to be dyed and let that bugger soak. Be careful washing it with other stuff for awhile though. I would imagine there may be some transfer to other clothing if you weren't careful at first. I don't know for certain, but hey, worth a try.