John Rivera asked on Facebook:

Is Carteret Blue a shade of blue, or is Carteret a brand of coats? A web search suggests that Carteret Blue may be a very bright medium royal blue, similar to International Klein Blue. Depending on what shade of brown you want, you can produce brown by overdyeing blue with an orange dye, or with a brown dye.

However, it may not be possible to dye your coat. Most coats intended for outdoor use are treated with a DWR (durable water repellent) finish, which rejects dye altogether; this finish is frequently not mentioned on the label or in any promotional materials about the coat. Even after a DWR-coated garment has gotten so dirty that it is no longer water resistant, the coating is still there and still repels dye. Washing and drying such a coat will often restore at least part of the water repellency.

In addition, there is the extremely important question of what fiber the coat is made from. A polyester coat, even if it has not been treated with a DWR finish, cannot be dyed except by boiling it for some time in a very large cooking pot with a special kind of polyester dye called disperse dye. If any part of the coat is made of polypropylene (popular mainly for socks and high-tech undergarments, but possibly also to be found in some linings), it cannot be dyed at all with any sort of dye. Spandex, a fiber used to make fabric stretchy, should be protected from high heat, so it's not good for dyeing if it is combined with polyester. Nylon is best dyed with a type of dye called acid dyes, which will not color polyester or cotton, while cotton is best dyed with reactive dyes but can also be dyed with several other types of dye that do not work on polyester or nylon. You can expect the trim, such as zippers, knit cuffs, stitching, and buttons to remain the original color after you dye a cotton jacket; would having blue trim ruin the look of your jacket, once it is brown?

If you tell me what the fiber content of your jacket is, I might be able to supply more information, but you should first check for a DWR finish: sprinkle a few small drops of water on the coat. If they bead up on the surface, rather than soaking immediately into the fabric, you should forget about dyeing the jacket and find a way to buy a new one.

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