You might split the difference and go with Black Americans. No one is likely to get mad about that sort of thing in an undergrad paper so long as you're making a good faith effort. Also the general trend is to capitalize the B in Black Americans these days, though that is a hot topic.

Just be consistent. Most writings on race use black with little to no qualms, but I think it comes down to your own stylistic decision. To me, African American or Black American is quite clunky, and if the paper is on America, highly unnecessary unless your work is transnational in nature. In regards to the last comment, if you do capitalize the B in black you need to capitalize the W in white, in my opinion for consistencies sake, and I haven't read anything convincing on why one would be capitalized while the other not. I don't capitalize either when writing, but ultimately that is your decision to make.

It might be no harm to ask your tutor or professor for advice on what is recommended in your department.