Lighter, I think it's possible (though I think genitive isnt the correct grammatical in this instance), The spelling would then be Ráithín.
Raithin (with no diacritical marks) and Ráithíneach don't really sound that similar. I don't know why none of the lyric transcriptions I've seen of the song have í rather than i. Do you hear ratchinach or ratcheenach (transliteration)?

Ráithín ia the diminutive form of ráth - an earthen ring fort
There are a lot of places with the name Ráithín in them
http://www.logainm.ie/ga/s?txt=gls:127-r%c3%a1ith%c3%adn

and we can form words with "ach" to say that someone is from a place, for example "Conallach", a native of Tír Chonaill (Donegal)
And as I said before there are also place names based on the plant name raithin, as in Cúil Raithin (no mark, no een sound)

What Jim Carroll is thinking of would be Rioghnach or Ríonach, a woman's name, which means queen-like.