Well black girls (African American is an inaccurate term as it applies to people actually from Africa, no offense) are the least likely statistically to date outside their race. Compounding this is that black culture frowns on black people, specifically the women from dating outside their race. Also it is a perceived class issue as Asian and whites are perceived to be upper class, and blacks and Hispanics are lower class, so a perceived class boundary is also in the way. Finally Asian people in general are very likely to stick to their race, and Asian men generally like to be in control in a relationship, where as black women are seen to be bossy and have an attitude, which makes them undesirable to Asian guys.
I believe all of these factors influence the extremely low numbers of black girl/ Asian guy couples, as opposed to the most common interracial couple of Asian girl/ white guy who don't have the issues (perceived and not) affecting their pairing.
I hope this helps and please understand this is a politically incorrect, but ultimately correct assessment.