Adding more versions to the pot.

Three Ships (Iona and Peter Opie)

I saw three ships come sailing by
Come sailing by, come sailing by,
I saw three ships come sailing by,
On New Years Day in the Morning.

And what do you think was in them then,
Was in them then, was in them then?
And what do you think was in them then,
On New-Year's day in the morning?

Three pretty girls were in them then,
Were in them then, were in them then,
Three pretty girls were in them then,
On New-Year's day in the morning.

One could whistle, and one could sing,
And one could play on the violin;
Such joy there was at my wedding,
On New-Year's day in the morning.

Probably derived from this version of the carol:

I Saw Three Ships

I saw three ships come sailing by,
Come sailing by, come sailing by.
I saw three ships come sailing by,
On Christmas day in the morning.

And who should be in those three ships,
In those three ships, in those three ships,
And who should be in those three ships,
But Joseph and his Lady!

And he did whistle, and she did sing,
And she did sing, and she did sing,
And he did whistle, and she did sing,
On Christmas Day in the morning.

And all the bells on earth shall ring,
On earth shall ring, on earth shall ring,
And all the bells on earth shall ring,
On Christmas Day in the morning.

And all the angels in heaven shall sing,
In heaven shall sing, in heaven shall sing,
And all the angels in heaven shall sing,
On Christmas Day in the morning.

Martin Shaw and Percy Dearmer, The English Carol Book, 1913, 2nd Ser.
Revised from a folk version (?) but seems to express the same ideas as the Ritson song quoted by Masato.

Origins? Sticking my neck out-
The Ritson version and "All Sons of Adam," to me, suggest that St. Michael and St. John were on board, and "our Lord harped and our Lady sang to welcome them.
Continuing to guess, someone with no knowledge of geography then put "Joseph and his Lady" aboard and created the anomaly.

Some have speculated that the three ships were bringing the Three Magi to Jerusalem (Matthew 2.1-2), but there seems to be no version with this thrust.

The nursery rhyme versions seem to be late; Victorian.