Another drifter that has sometimes found lodging in this song:

Raccoon has a bushy tail,
Possum's tail is bare,
Rabbit ain't got no tail at all,
Just a little bitty bunch of hair.

The second tease stanza quoted by Amos also appears expanded as a recitation:

Of all the fishes in the seas,
The strangest is the bass.
It climbs into the tops of trees
And slides down on its hands and knees
To frolic in the grass.

The one quoted by Les B likewise appears as

Mary had a little watch.
She swallowed it one day.
The doctor gave her laxative
To pass the time away.
Mary took the laxative,
But the time, it would not pass,
So if you want to know the time,
You can look up Mary's aunt, who has a watch too.