I stumbled across this thread while looking for something else and decided to refresh it to post the melody of the song.   It is, as Alison ironically comments "another cheerful little ditty about Belfast". The melody is, as Malcolm Douglas points out, a variation (I nearly said "corruption") of "The Dolphin" which can also be found in "The Singing Island" by MacColl and Seeger. The words listed above are not 100% but pretty close. Line 3, Verse 1 should read, "Our town's an old sandcastle and the waves begin to pound". I haven't heard Mick Moloney's version but the tune I give here is taken from the guy who wrote the song.   One difference is that in the traditional tune the notes C in bars 14 and 26 are natural not sharp.

X:1
T:LEAVING BELFAST TOWN
M:3/4
Q:140
K:D
A|d2d|d2e|d2c|d2e|f2g|f2e|d3|z2f|g2g|
g2g|f2g|a2f|e2d|c2B|A3|z3|aaa|fed|B2g
|g2g|f2f|edB|A3|z2A|B2B|cBA|d2d|efg|a2f|efe|d3|z2