LITTLE DAPPLED COW, sung by Texas Gladden, is included in a 4-CD compilation of Alan Lomax's field recordings called "Sounds of the South," Atlantic CD #82496, 1993. It seems to have no connection to THE SPOTTED COW, which is in the DT.

From CDNOW's sound sample, I was able to transcribe the following excerpt:

...When she fell down on the cow
And she stumbled o'er the plow
And the cow was quite astonished at her screaming-o.

Little maid cried out in vain
As the milk ran o'er the plain
And the piggy went a-grunting oh so gaily-o
And the little dog behind
For his share was much inclined
So he...

I found the following version embedded in a memoir by Dixie Almond Smith at
http://www.geocities.com/Heartland/Valley/6368/Almond/dixiestory2.html
She recalls singing it in Oregon in the 1940s.

OH THERE WAS A LITTLE MAN

Oh, there was a little man,
Where a little river ran,
And he had a little farm and little dairy-o,
And he had a little plow
And he had a little dappled cow,
That he always used to call his little fairy-o.

Now his pretty maiden, Nan,
With her little milking can,
Went a milking when the morning sun was beaming-o,
And she fell, I don't know how,
And she stumbled o'er the plow,
And the cow was much astonished at her screaming-o.

Little piggy ran in vain,
As the milk ran o'er the plain,
For to gather up the milk was piggy's pleasure-o
Little doggy, much inclined,
Came a sneaking up behind,
And grabbed the squealing piggy by the taily-o.

Now to make a story short,
Little pony with a snort,
Gathered up his little heels so very clever-o,
And the man he tumbled down,
And he almost broke his crown,
And that just made the matter worse than ever-o!