Human hair dye will not work with doll hair. Try one of the methods suggested below.
Using Acrylic Paint: My favorite method, easy, safe, non-staining, yadda. Water the acrylic paint to an ink like consistency. Make sure the hair is clean with no conditioners or hair products in it. Wrap the doll in a saran wrap cover to protect her body and neck. Pile the hair up on her head, comb the watered paint through her hair starting at the base of the neck and working toward the hairline in thin sections - comb frequently while drying. If paint gets on her face during this process it can be easily removed with non-acetone nail polish remover. - If the color ends up too pale you can repeat the process as many times as necessary. AFTER the hair is completely dry 'heat set' the dye. Hold the doll upside down and heat the hair with a blow dryer ON LOW - style as usual. The drawbacks The hair will be somewhat stiffer after it's been 'painted' and also won't have much 'shine' to it. Hair styling products can interact with and/or remove the dye. Dye may flake or fade over time. Here's a better 'step by step' for Acrylic 'dye': Doll Raves Using acrylics as hair dye.
Using Kool Aid: I've never actually tried this - but here goes. Wrap your doll in saran wrap and rub vaseline on her face to try to protect it. Make the Kool Aid (unsweetened!) per instructions with boiling water. Hold the doll upside down making sure the hair is brushed out and very carefully dip her into the Koolaid until you have the desired shade. Keep in mind that sythetic hair plays 'wick' really well and will draw the dye up. Allow to dry upside down and then wash and style as usual.The drawbacks The odds are very very good that you'll dye the face as well as the hair. Koolaid doesn't come in 'normal' colors and mixing it is um..... If it's not washed out *very* well the hair will proceed to dye the dolls body, your hands, her clothes.... etc. etc.
Using Leather Dye: Don't...... just....... don't.