My daughter and granddaughter have dark hair. My granddaughter's hair sounds like the color of yours. It's nearly black. It only looks somewhat brown in the sun. She colored her hair at a salon twice. The color didn't show up on her dark hair the first time.The next time she went to a different salon. They bleached out parts of her hair first. The bleached out hairs colored fine. The rest was a very faint blue, hardly noticeable. My granddaughter now colors her own. She bleaches a few sections first. The part she doesn't bleach remains her natural color.
My daughter's hair looks dark brown. She colors her hair at a salon. Her hair has a reddish tint. The parts she bleached are more red. All of her hair is a subtle red and is natural looking. Once she tried coloring at home, didn't like the results. She colored her hair with a home product back close to her natural color. She waited until the color was mostly gone to go back to read salon for coloring it red once again.
When my hair had noticeable gray, I had it frosted in a salon. No bleaching. It looked great. In my job hair had to be a natural color. This was acceptable. Eventually, I colored it myself, using an inexpensive frosting kit.
I suggest you go to a beauty supply store such as Sally's and ask for advice. Their clerks are trained beauticians. If your hair has just a few grey hairs the color may not show up. A beautician could look and feel of your hair to tell you.
I think it's best to have coloring done by a professional because I can see how they do it.