From a blog somewhere:
"Okay - as my mother explained to me many moons ago - 'sheep's eye and the licorice tooth' are like a young kid making 'calve's eyes' at a girl he likes (sort of mooning over her, as it were) and licorice tooth refers to the sweet tooth. She was old enough to remember Damon Runyon when he was alive, and was raised in the Bronx, so she basically knew that area of NYC."
From program notes somewhere:
"In the original Frank Loesser score, the expression is "sheep's eye and the LICKERISH tooth." Loesser explained how he arrived at it in a letter that's printed in his daughter's fine biography of him, A MOST REMARKABLE FELLA (page 109). The short of it is that he wanted a companion word that meant "covetous", fearing "sheep's eye" did not completely convey the exact thoughts of the guy who would be gazing at her. He went to Roget's and found that "lecherous" was a sort of synonym for covetous, but didn't quite like the way it sounded, so he consulted the Oxford English Dictionary and found that two archaic spellings of "lecherous" were "licorice" and "lickerish." He chose the latter.