Song that Sellers sings

When Sellers dresses up as an Irishman and goes into the pub, he sings a little song, "'tis the Shamrock in her hair that reminds me of Killarney".. is this based on any real song? In other words is there a similar song and he, (the character) doesn't really know the words and is kind of making it up as he goes along, or is it a totally made up song for the movie. The tune sounds very familiar!