I don't live in the US, so this is just based on something I recall reading, but "African American" can also be seen as more offensive than black (and most prefer black). Most "African Americans" have little to do with their African roots (if they even have African roots). Having a quick google search on the topic shows most people feel this way, and that "African American" sounds like you're trying to hard to be PC - which in turn can be more patronising.
Is it important in your script to make a clear distinction of races? Most people don't really want to be labelled by their race/skin colour (how often do you hear someone referred to as a "white american" or "Caucasian"?) - but obviously if there's a reason for it in your story, go ahead.