Quoted from PinMagnet:Man do I hate the term "person of color". African American will do just fine.
Not to get all semantics on you, person of color refers to all people who are not “white” or of European descent. This would include not just black people but Indians, Native American, Hispanic, middle eastern, etc.
African American will do just fine but you can also say black, it’s perfectly acceptable. Many black people cannot trace their heritage back to their specific country of origin due to slavery and actually prefer the term black and dislike the term African American, I doubt you would offend anyone using that term though.