My guess is that "He's got a woman down the hall and I think he wants me anyway". is easier to sing (and seems a little less clunky) than "He's got a woman for the night and I think he wants one for the day". It also changes the meaning a little-the new lyric implies having a string of lovers/girlfriends as opposed to having a series of one night stands.
RE: ...Some of these recordings are available and are very interesting. Joni does "Woman of Heart & Mind", "Edith & The Kingpin", "Don't Interrupt The Sorrow", and an early version of "Coyote" where she sings the original lyric: "He's got a woman for the night and I think he wants one for the day" instead of: "He's got a woman down the hall and I think he wants me anyway". Wonder what prompted that lyric change? Send FREE video emails in Yahoo! Mail! http://promo.yahoo.com/videomail/