My mom sang this when I was a kid - this site had the only near match:

"...Shot his sister?, when he was only three
Drownded his brother in a cup of tea
Davy, Davy Crockett, King of the Wild Frontier..."

I think she said the original was "shot a b'ar" which was supposed to mean bear.

While I'm at it, this one she sang recalls a better-managed time...

"Beer, beer for old Stroudsburg High
You bring the whiskey, I'll bring the rye
Send somebody out for gin
Don't let a sober senior in!
We never stagger, we never fall
We sober up on wood alcohol
? ? ? ? ? ? ? and open the guldarn bar!"