As Eric pointed out, there were a number of parks that were purpose-built for Negro league teams, such as Pittsburgh’s Central Park, originally constructed to house Sell Hall’s American Giants in the summer of 1920. By 1921 the park’s owner, Alexander “Don” Williams, had founded his own Pittsburgh Keystones to play there.
Kevin Johnson has found a Sanborn fire insurance map showing another: Lewis Park, the home of the Memphis Red Sox. It was built by Robert Lewis, a funeral home director who owned the Red Sox in the early 1920s. In the 1930s it was renamed after new owners, the Martin brothers, one of whom (J. B.) eventually became president of the Negro American League. Lewis/Martin Park would house the Red Sox for forty years.