I have been singing this for about 25 years, with concertina accompaniment. It makes a great ender to an evening when everyone sings the chorus. I learnt it from an old singer in Gloucestershire and later recorded Johnny Doughty singing it. The chords I use are:

C G C C7 F / C / F Am C Em C F/G C (repeat)
middle eight: F / C / G / C C7 F / C Em Am / G G7 (back to 1st line).

This fits the words:
Goodbye, old ship of mine.
No more you'll cross the line.
Well, your days are through sailing on the blue.
Goodbye, old ship of mine.

When they break you up at dawn,
In the yard where you were born,
They will break a part of a sailor's heart.
Goodbye, old ship of mine.

(middle eight):
Well, your logbook I'll keep as a token
In memory of you, Mary Ann.
I'd give the whole world just to keep you,
Oh but I'm just a poor sailor man.

So goodbye, old ship of mine,
For the sake of Auld Lang Syne.
Your name will still live on 'til the day I'm gone.
Goodbye, old ship of mine.

Good to see the info about the origins of the song.

Tradsinger