Yes you can use black to make your green paint a darker shade of green. White paint to make it a lighter shade of green. Blue and yellow combined make green. I gather oyu bought the paint from a paint store, take it back and ask them to make it a shade or two darker. They should be able to scan a color swatch and compare it to a color your after, the puter will compare the two and tell the tech which color and how much to add to get the color you want. He may have to add a combination of black/blue and maybe a touch of white to get the shade you want.
If you just want to mix it at home, black will give your a darker color- more towards a black green. If you add a dark blue youll get a draker green more towards the blue side.
When you reply to this thread notice the Font colour bar on the right side. Teh bottom grid is mostly red/yellow, the next grid up has a touch of blue added, as you get to the top grid black has been added. There are only 4 color in that grid, cmyk.
c=cyan=blue
m=magenta=red
y=yellow
k=black.