Depends what kind of cousin you're talking about. Let's go with a first cousin. That is, you and your first cousin share one pair of grandparents.
Your niece is your cousin's first cousin, once removed.
a daughter, Carol
, and a son, David
Carol's child is you
. David's daughter is Fran
. Fran is your first cousin.
Let's say Carol has a second child, George
. George is your brother.
George's daughter, Heidi, is your niece.
If Fran has a child, Iris
, then Heidi and Iris will be second cousins.