i'm assuming its some type of regular fabric? you can usually get fabric dyes at drug stores. check shoppers drugmart or like... pharmasave... i dunno. hahah. the dyes are pretty cheap. im not quite sure how to use them but i'm sure its not too hard.
If you plan on washing it you need to water down the dye, or wash it for the first time alone, unless you want a tie dye effect on the other clothes being washed with it, it happened to me before hahaha. Very good way to do it though.
I have a cotton jacket that started olive green and I used a fabric dye on, but just that probably won't be enough to make it really black, mine is somewhere more like black olive and purple, its a hard color to explain.
spray paint works well, or they have these fabric dyes that you spray on, usually used to design craft shirts, or you could just have a fight with some black hair dye. you can find cheap brands and that shit never washes out of my clothes.