Short answer: no, he wasn't. But that is assuming that by "black" you are referring to African American in the contemporary sense, and obviously Beethoven himself had little relationship to American racial discourse. But was Beethoven of African descent, or have dark skin? Possibly. His maternal ancestry is not firmly-established by scholars, and as Michael Broyles explained in a paper this morning, there have long (since at least 1907) been persistent rumors that Beethoven's family tree involved descendants of Spanish Moors who were once stationed in the Flemish region his family was from. So, the long answer is, maybe.
The paper Broyles gave this morning covered these biographical issues briefly, but was more concerned with how the trope of "Beethoven was black" was used in radical black politics in the 1960s. As with a number of other figures--Jesus probably being the more famous one--putatively white cultural touchstones were mobilized by some black nationalists as examples of a suppressed black cultural heritage. Broyles primarily looked at various writings by figures such as Amiri Baraka, and also noted examples of radio stations that used the phrase "Beethoven was black" as a call sign, the infamous Ujamaa House incident at Stanford, and the track "Beethoven" by the rap outfit Soulja Boyz.
Unusual for a paper at AMS, there were some pointed critical comments afterwards. After one audience member described the paper as "wonderful," Guy Ramsey--the well-known scholar and practitioner of African American music at Penn--stood up to say that the paper might be cool, but it wasn't "wonderful." Ramsey mostly picked at the examples used, especially pointing out the diversity of black nationalism. A more provocative comment came from Richard Mook of Arizona State. He lit into the choice of the Soulja Boyz song, asking what this had to do with black nationalist appropriations of Beethoven's heritage. He didn't say this exactly, but I think he was suspecting that Broyles had simply found a random example of a black person listening to Beethoven--as Rick rightfully said, highly problematic. I would also point out that there was no ethnographic component to Broyles's paper; many of the people he discussed are alive, and rather than relying upon the bits of writings here or there, it would be interesting to actually ask them about it as well. If you're going to write about the recent racial past, it's best to, you know, actually talk to the people who were involved.
Another respondent whose name I didn't catch voiced what I had been thinking, that this wasn't really a paper about blackness. Rather, the idea of a "black Beethoven" forces us to name whiteness. If Beethoven wasn't black--and that's the reaction most have to the titular question--than you have to say what he was, which is to say, white. As my friend pointed out afterwards, many people like to believe in the universal appeal of Beethoven. If his music really was transcendently universal, than it wouldn't matter what race he was. And yet the visceral, violent reaction to the idea of a black Beethoven, a reaction disproportionate to the issue at hand, shows that for many people it is actually quite important for him to be white.
The interesting question here is not why black radicals in the 60s used Beethoven--I think that the cultural work being performed by that intellectual position is pretty obvious. One only need to look at the furious and overtly racist reactions from the 1960s to see how well it did its job of exposing covert rhetorics of white superiority. And to be perfectly honest, one might also look at the session itself: There were probably about 150 musicologists seeing this paper, and as with any session at AMS, those musicologists were overwhelmingly white. I think that might possibly explain one audience reaction to Broyles's paper that I found occasionally disconcerting: anytime he quoted one of the black nationalists claiming a black Beethoven, the audience responded with laughter. Whereas the threat of a black nationalist Beethoven was a very real one in the sixties, our contemporary audience was confident enough in the whiteness of Beethoven that we can find it amusing. I'm not sure that's progress!
13 hours ago