If My Cousin Has a Baby, What Am I To That Baby?
Technically, your cousin's baby is your first cousin once removed. This means that you and the baby share a common set of grandparents.
What does “Once Removed” mean?
Being once removed simply means you are in different generations. In the case of your cousin’s baby, you are one generation older than the baby, or "once removed."
What does My Cousin’s Child Call Me?
Your cousin's child would technically refer to you as their "first cousin once removed." The "once removed" indicates the difference in generations. However, greeting your cousin’s child by saying “Hey, first cousin once removed!” doesn’t really slide off the tongue, so many people either call their cousin’s children nieces/nephews and have the child call you an aunt/uncle or they just go for the term cousins. As there may be some sensitivity here, it is always best to check with your cousin as to how they want you to refer to their child. Either way, you should seriously consider buying a custom onesie and maybe matching custom shirt that says "New to the Cousin Crew", "Cuz", "Cuz 1R" or "My Fake Uncle Rocks" or something clever like that.
So, What is My Child to My Cousin’s Baby?
Your cousin's baby is your child's second cousin. This is because your child and the baby share a common set of great-grandparents.
Family Relationship Chart
This chart really helped me better understand all of the familial relationships better.