What You'll Need
1 bottle vodka
10 drops blue food coloring
10 drop red food coloring
8 drops green food coloring
How to Make It
Add food coloring drop by drop to a bottle of vodka.
Seal the bottle and shake well. Store as you would any other vodka until you're ready to mix a drink.
Tip: You may have to shake the bottle again before pouring a drink because the food coloring may settle.
DIY Black Vodka Is Not Perfect
This is a quick gimmick and it is, admittedly, not perfect. The actual color of the finished vodka, when poured into a glass on its own, is not a solid black.
Instead, it has a transparent, tinted black "water" look that may have a red, green, or blue hue along the edges. However, for its purposes and as long as it takes for you to mix then consume the drink, it will work.
If you're just playing with this idea, begin with a small amount of vodka in a glass (keep the 10:10:8 drops) and see if you like the effect. There's no point in wasting a full bottle if it won't work for your needs.
How Black Will Your Cocktails Be?
If you are trying to bring a non-black drink into the darkness, do some experiments first to see if it will give you the look you're going for. Depending on the mixers in the drink and their proportions, this black vodka should at least turn it a darker hue, though it is not guaranteed to turn the entire drink black.
Try a Black Rice Infusion
There is another option that you might want to consider, though it requires a specialty ingredient and a few extra days. It may not be the best solution if you're short on time or cash. The real trick is finding the black rice, which is available online or at a few specialty markets and it is not cheap.
Once you have the rice, simply infuse it into a bottle of vodka. Use a generous amount of rice (at least 1 cup per bottle) and plan on at least three days for the infusion. Give it a good shake at least once a day.
As the infusion ages, you should be able to easily gauge the results. Once the vodka has reached the desired color, strain the rice, and re-bottle your new black vodka.
This method results in a vodka that has a nice, black color and the taste is unaffected. You also don't have to worry much about colors settling, though shaking the bottle before every pour may still be a good idea.