I suspect that the impulse to use “urban” was the same for the radio programming and the Urban League. The Urban League was specifically founded to help blacks, migrating from rural, agricultural settings in the South, to urban, manufacturing settings in the North, adjust to and be successful in their new environment. Similarly, the “urban” music was music that was directed to an audience that was very much located in the inner cities.
(It probably did not hurt that the “Country” music is, stereotypically “white,” providing an easy contrast in the names.*)
While the Urban League, itsel, is very old, the use of urban to indicate a “black” experience did not become common until after Urban Radio popularized that use of the term.
- (This is not a claim that all whites listen to only Country (and Western) or that there are no blacks performing in or listening to that genre, only a recognition–even if stereotypical–that Country is more of a “white” genre while Rock and Roll, Jazz, and Pop include many artists from each group and are popular among audiences of both groups.)