It's quite simple. The original song was written for a 1929 movie "Gold Diggers of Broadway". The movie is exactly as it sounds; it's about a bunch of women who have a struggle between finding a man they love, or a man who's rich. The song appears after a night club scene and is supposed to 'cheer everyone up', I guess (never seen the film, just going off of the wiki page).
But the themes of the song and events in the movie are juxtaposing. The song is very romantic; the ideas of love, nature, free spirit and spirituality in general are present in the song, alongside its soft, sweet tone. However, this song appears after a lustful, nightclub scene (not very natural) with women dancing on tables, trying to marry (not very free spirited) a man who's at least financially stable and, at most rich (not that idea of love). I guess the song is there as the rich men are tricked into believing they're genuinely loved.
Tiny Tim's version obviously has those same ideas of love, spirituality, freedom and nature that are similar to the romantic movement. This is evident in some of his other songs ("Fill Your Heart" and "Earth Angel"). So I guess that's all that the song really means. It's kind of a long answer for a simple response but that's probably just what it means. Tiny Tim didn't change much in the way that Dead Kennedys did with "I Fought the Law" so it probably has the same themes, without the movie's context.
I don't think it's about child rape though.
