Dye is transparent, so it cannot cover up the original color of the garment. If you try to overdye dark green with dark purple, the best you can get is a dark brown.

If you want to dye your dark green jacket, try dyeing it a dark brown or black. Nothing else is going to work.

If you want a dark purple jacket, start with a jacket that is white, off-white, blue, pink, or light purple.

Also note that you cannot dye anything that is not washable. Prewash your jacket first; if it does not survive washing, then it was not dyeable. Lined jackets are almost never washable; the outside will shrink more or less than the lining does, ruining the shape of the jacket.

The fiber content of your jacket is crucial. You will not be able to dye synthetic fibers such as polyester, acetate, or acrylic, unless you mail-order a special polyester dye called disperse dye and then boil your jacket in the dye for an hour, a process that will destroy most ready-made garments. You can dye washable cotton, linen, rayon, silk, or hemp; best results will come from using a fiber reactive dye, such as Procion dye. All-purpose dyes such as Rit fade quickly and bleed badly in the laundry when washed.


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[Portions of this answer were first posted, by me, on Yahoo answers, on September 30, 2008.]