1. Sugar rolled up in a handkerchief held together by a piece of string for a baby to suckle on.
Used primarily in situations where you are attempting to quiet a child. (and give it a set of rotten teeth as they come in)
2. Something Grandmom yells when she is upset
Example 1: "I gave my baby a sugar-tit to quiet it during the movie.
Example 2: "oh sugar-tit!"