This has been an interesting evolution in the church I attend. For the most part, the under-50 educated white crowd has come to accept/believe that African-American is the safest term to use, and my church is heavily under-50 educated white, so that has been the norm there.
However, through some unexpected circumstances (i.e. there was no "church growth" or "outreach" strategy that made this happen..it just happened,) our church has pretty much become the go-to church in Greensboro for Christian refugees and immigrants from East Africa, a significant percentage of whom have now been here long enough to become American citizens. (It's not like there are a TON of those in GSO, but enough that we have a service in an East African language that meets on Sunday afternoons that is typically attended by 30-40 adults.) Of course, these true "African-Americans" are culturally vastly different from us regular ol' American black folks, so it has been (at least to me) fairly humorous to watch white people twist themselves into a pretzel to try to avoid saying "black" when talking about strategies for better outreach to black folks vs. Africans. I think "ex-Africans" (speaking of the refugees/immigrant population) has been my favorite one so far.
I've always preferred "black," partly because it's easier, and partly because I've known several white "African American" South Africans. Talk about confusing...