I tried to draw some sprites a while a go, and from what I gathered the tricks are: 1) placing your highlights/shadows to create volume (check the "pillow-shading" part on this page for a better explanation) 2) using different hues in your palettes, perhaps even more so than with traditional drawings (see this tutorial for an example of how to do that 3) if possible, using combined palettes - I don't know how to explain that one, basically when two different base colors share a shadow, or stuff like that.
Try checking some experienced spriters on DA, or maybe spriting communities outside DA, I remember finding some good tutorials out there.
1. Pick color that's darker than the base color 2. Pick the base color as the secondary color 3. Use the color replacer tool
But, your question shouldn't be just limited to sprites. Shading is a technique that is shared across all mediums. You can just try out a cel-shading style of shading which is far simpler to work with. You do not need a gazillion different colors or a lot of gradients to shade.
I don't think using transparent black to shade is a great idea. I usually shade using 3 colors- the base color, a lighter version, and a darker version. Then you just pick a light source and shade like it's a regular drawing. Just don't try and get too fancy.
I don't know what you mean by sprites, but when I colour in photoshop I like to use a colour like black and then reduce the opacity. When you do this the paint becomes transparent and you can then use the colour to shade areas without completely colouring them in or losing the image underneath. You can play around with the opacity to get different depths of shade.