I'm afraid the only answer to this question given so far is absolutely wrong.
Song lyrics should always be attributed to their actual author, not a performer. Just like you wouldn't even think of attributing a quote from a play to an actor instead of the playwright, you shouldn't attribute Where Have All the Flowers Gone to Marlene Dietrich or Joan Baez or any of the dozens of other singers, you need to attribute it to Pete Seeger.
If you quote,
I heard there was a secret chord
that David played and it pleased the Lord
but you don't really care for music, do ya?
then you don't attribute it to John Cale or Rufus Wainwright, you attribute it to Leonard Cohen.
In some contexts, such as performing it live at a concert, the author's name may go unmentioned, but the authorship should never be misattributed. A cover version being "more well known" than a recording by the author themself (if it exists at all) is no excuse. It's still the same song, you aren't attributing the arrangement and performance, you're attributing the lyrics.
If you include a song quote in a published written document, then you generally should give both the title of the song and the name of the songwriter.