Btw, it's interesting to find that "I went to the river and I couldn't get across" verse in that song/rhyme. That verse is found in a number of 19th century or earlier African American secular slave songs. Here's one widely quoted example

I went to the river,
And could n't get across;
Paid five dollars
For an old blind horse

Dorothy Scaborough, On The Trail of Negro Folk Songs {Hatsboro, Penn.; Folklore Associates, Inc, 1963, p. 185, originally published, 1925, Harvard Univestity Press}

Here's another one from that same collection:

I went to the river
And I could n't get across.
Jumped on an alligator
And thought it was a horse

-snip-

Since Vaudeville was mentioned in that response quoted in my previous post, and since one of the sources for Vaudeville was American minstrelsy {http://en.wikipedia.org/wiki/Vaudeville}, and and since the minstrel shows borrowed heavily from African American traditions, I believe that African American songs were the original source of the "I went to the river and couldn't get across" verse that may be found in "Aunt Mary Had A Canary" songs or rhymes.