Both Ewan McVicar and Arthur Johnstone claim it was Luke Kelly who married the tune to the words. Luke's own account seems to contradict this:
[1994:] Luke told the following story in an interview in 1980: 'I was sitting in a pub in Dublin, The Bailey, and as you know in the old days - it's changed a bit now - it was known as a literary pub, an artistic pub. I happened to be sitting there in the same company with Patrick Kavanagh and one or two other poets, and someone asked him to recite a poem, which he did, and then someone asked me to sing a song which I did. Being in the presence of the great man I was very nervous. Then he leaned over to me and said in that sepulchral voice of his - he could hardly get his voice out, he was very old ... it was just the year before he died - and he said 'You should sing my song,' and I said 'What's that, Mr Kavanagh?' and he said 'Raglan Road''. So he gave me permission. I got permission from the man himself.' (Geraghty, Luke Kelly 38f)
If Kavanagh talked of his 'song', it is reasonable to assume it had a tune already. Perhaps it was a different one originally? But wouldn't Luke have mentioned it if he put a different tune to it?