There are a number of companies offering what they call water-based dyes to use on nylon automotive carpet, but you must be careful.
Nylon-carpeting fibers are dyed in the mills with an acid-based dye that must be "heat-activated" to permanently bond to the fibers. Many companies tell you to use hot tap water. That is false information, as the dye solution must be heated to over 160 degrees F. So, unless you have a way to heat the dye solution to this temperature, you are taking a chance the application will not be permanent.
There are systems available where the dye is pumped through an in-line heater, similar to what is used in a heated soil extractor, to heat the dye to 160 degrees F. The benefits of such systems are organization and simplicity of use for the operator and conservation of dye.