I found this in "The Fireside Book of Fun and Game Songs" c1974, Simon and Schuster, Marie Winn, Editor. The song is not attributed. Verses for 6 through 10, as mentioned by DrWord, weren't there...Tiger

ONE MORE RIVER

Each stanza has "There's one more river to cross" as second and fourth lines.

Old Noah built himself an ark,
There's one more river to cross;
He built it out of hick'ry bark,
There' one more river to cross.

CHORUS (after each stanza)
One more river,
And that's the river of Jordan;
One more river,
There's one more river to cross.

The animals went in one by one,
There's one…
The elephant chewed on a hot cross bun,
There's one…

The animals went in two by two,
The anteater and the kangaroo,

The animals went in three by three,
The monkey and the chimpanzee,

The animals went in four by four,
The hippopotamus stuck in the door,

The animals went in five by five,
Noah's sons and all their wives,

And as they talked of this and that,
The ark bumped into Mount Ararat,

Oh, Mrs. Noah she got drunk,
And kicked the old gentleman out of his bunk,