From Wikipedia:
By kissing the Blarney Stone at Blarney Castle, it is claimed that one can receive the "Gift of the Gab" (eloquence, or skill at flattery or persuasion).
I'm not terribly familiar with the song (or the country, for that matter) so it's quite possible I'm on the wrong track, but it seems to me that 'Blarney' in this context might be a slang term for the 'gift of gab' referenced above.
Edit: Alternative explanation: 'blarney' actually means 'the little field' in Irish. When you take that with the line 'Nature bestowed all her gifts with a smile', it fits in with the rest of the list, which are natural things.