I think Freddie Rodriguez, the actor who used to be in Six Feet Under, might have been a good alternate Spider-man, while Freddie Prinze jr was quite anxious to play the character when they began casting in 2000 or so. And yes, there are probably a few black actors who could playa good alternate Spidey.
The question is, though, why bother? Why not depict him as he's traditionally been portrayed? I mean, I can understand and support casting Michael Clarke Duncan as Kingpin, because I can't think of a white actor who could be as convincing a Wilson Fisk as he is. And Ben Grimm's girlfriend in Fantastic Four could undergo a colour change because she's not really an iconic character and if a black actress can play her as well, then well and good.
But with someone like Spider-man/ Peter Parker who is quite iconic and who has a long-standing visual representation - from a medium which is primary visual - why just change his ethnicity for the sake of it? I'm just not persuaded that there's a need.
I think there is much more merit in creating a new black superhero. To give an example, when walter Mosely wanted to have an African-American take on the noir genre, he didn't take Sam Spade or Philip Marlowe and make them black. He created Easy Rawlins, an original black private eye.
Now, Easy is regarded as one of the greats of crime fiction, not just the modern version but of all time. Had Mosely simply written a series of novels with a black version of Marlowe or Mike Hammer or whoever, would they have become so acclaimed and definitive? I don't think so. Would the Blade movies have been any better had Blade instead been called Van Helsing, but with a black man playing the lead? Doubt it.