Recorded by Iona Opie back in the 1950s in the UK:
As I sat under the apple tree
a birdie sent his love to me
and as I wiped it from my eye
I said "thank goodness cows can't fly!
This morphed into one that was current in the States by the end of the 60s:
Birdy, birdy, in the sky
dropped some whitewash in my eye
I don't worry, I don't cry
I'm just glad that cows don't fly!"
Several variations of the American version go around, more recent ones being somewhat more explicit and often leaving out the cow part altogether:
Birdy, birdy in the sky
Why'd you do that in my eye?
Looks like ice cream, tastes like spit
Oh my god - it's birdy s--t!
Generally speaking, these songs and rhymes don't get dirtier or more explicit as time goes by (often, in fact, it's the other way around) It's interesting that the American versions are not just dirtier, but much more simplistic than the British version - was it "dumbed down" as it crossed the pond? And how strange is it that I'm even talking about dumbing down a poop joke to begin with?