It's true, black right out of the tube is definitely black, but you'll find that a mixed black gives a beautiful depth and is much more interesting to the eye.
The easiest way to mix black is to take two colors opposite each other on the color wheel and mix them together: green/red, blue/orange, purple/yellow. As you mix, you may first get a shade of brown. That's how I mixed brown for my violin painting http://bearhollowcreations.blogspot.com/2008/09/mixing-brown.html But you'll notice on that painting that there are parts of the body of the violin that are dark and could become black with a little more of the blue added.
In this painting I used my favorite color combination for making black - red and green. I used alizarin crimson and veridian. Actually, I first painted the entire canvas with inexpensive black acrylic. This way I didn't have to worry about any white shining through the background. I then painted the entire background with liquin paint thinner. The liquin allowed me to cover all the background quickly and without using a lot of thick paint. (I wanted the calla lilies to be thick and didn't want them to have to compete with the texture of the background.)
I took my red and green and barely mixed them. I didn't want to lose all of the red or green. Using a criss-cross painting motion, I painted the background with my red/green mix. I don't think you can tell from this photograph, but the red and green can be seen here and there in the background. That's what gives the background some interest and some depth. I think I threw in a little blue here and there too. Not that you really see it, but I really love blue and think everything should have at least a little touch of blue.
So the next time your piece calls for black, see if a mixed black will do the job. You'll be very pleased with the results.