You can use non-transparent black as XanKriegor noted above. For the game, it's the color position in the palette that matters.
You can have two 0,0,0 blacks in the palette, however most image editing programs will take the index of the first occurrence of the color, which will be always #0. Therefore you need to choose any color other than black for the position #0 that you don't use on the same map for anything else. That will be the transparent color. Once you're done, save the map, then open your PNG in TweakPNG or a hex-editor to edit the palette cell #0 to black (0,0,0). Make sure that this only changes the palette table and not any part of the image data. Now the 0th black will be used for transparent areas, while any other black you have put in the palette will be used for solid areas. Note that if you later open the map for editing again, and save it, the distinction between blacks will be lost. So you best keep two copies of the map to avoid having to perform an undo operation on the cell #0.
Note that if you're making 32-bit Project X maps, things are drastically different. For those maps, PX looks at how deep the color is. 0,0,0 is fully transparent, although things like dark reddish blacks will have two states at once: being non-solid (intangible) and non-transparent at the same time. The exact threshold of color intensity has not been measured, also it may not have been intended and thus a bug in PX. PyroMan has used this technique to create maps with custom background pictures and texts.