The proper relation title for a cousin's baby is "first cousin once removed." Although "second cousin" is popularly used, it has a different connotation.
When properly used, the numbered terms for cousins such as "second cousins" represents the relationship between the children of siblings. This term is incorrectly used to describe the relationship between a person and the child of his or her cousin. Second cousins are the children of first cousins.
To properly reference the child of a person's cousin, the term "removed" is used because it identifies the generational difference. Specifically, the child of a person's cousin is one generation removed from the person himself or herself. The grandchild of a person's cousin is two generations removed from the person and so on.