Folks,
I once obtained the lyrics and the explanation for this song from Geoff Kaufmann (Forebitter), and then promptly lost my music book. However, I think I can recreate them. I believe the 'burton in the archway' had something to do with the way that they stored the barrels in the hold of the ship to prevent them from rolling. Sonnydore is obviously a woman (or a metaphor for one). I have the recording. Spellings not withstanding, here are the lyrics.

DOWN TRINIDAD

Tell me mister stevedore, how you stow your cargo?
Way-hay-hay sing Sunnydore
Tell me mister stevedore how you store your cargo?
Bound down Trinidad to look for Sunnydore

Chorus:
So boodgie free me bully boys, a burton in the archway
Way-hay-hay sing Sunnydore
So boodgie free me bully boys, a burton in the archway
Bound down Trinidad to look for Sunnydore

Oh Trinidad, Oh Trinidad you pretty little harbor
Way-hay-hay sing Sunnydore
Trinidad, Oh Trinidad you pretty little harbor
Bound down Trinidad to look for Sunnydore (Chorus)

What will you do with Sonnydore if ever you should find her
Way-hay-hay sing Sunnydore
Roll her in the grass my boys, all among the clover
Bound down Trinidad to look for Sunnydore (Chorus)

Well tell me mister barber, how do you shave your customers?
Way-hay-hay sing Sunnydore
I take 'em by the noses and scrape 'em on the chins-e-o
Bound down Trinidad to look for Sunnydore (Chorus)

So hoist her high, hoist her dry, roll me in the clover
Way-hay-hay sing Sunnydore
The ships all right, the crew is tight, the captain's all in clover
Bound down Trinidad to look for Sunnydore (Chorus)

So tell me mister stevedore, how you stow your cargo?
Way-hay-hay sing Sunnydore
Tell me mister stevedore how you store your cargo?
Bound down Trinidad to look for Sunnydore - down Trinidad to look for Sunnydore!