There may be no relationship. If you do not share a common ancestor, you are not technically related.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
You and your father's niece are first cousins.
They are first cousins once removed. Your niece's children and your grandchildren will then be 2nd cousins.
Your daughter and your niece are first cousins Your daughter and your great grand niece are first cousins, twice removed.
Your niece and one of your grandson's parents are first cousins. That makes your niece a first cousin once removed of your grandson.
Your daughter and your niece are first cousins to each other.
Your children and your niece are first cousins to each other.
You and your mother's niece are first cousins to each other, so your and the niece's daughter are fist cousins, once removed.
Your aunt's son and her niece are first cousins to each other.
Your grandchildren and your niece are first cousins, once removed, to each other.
Either they are second cousins or technically not related at all. Your cousin's niece would be one of her siblings' children, in which case it would one of your cousin's daughters, or her spouses' niece, in which case there is no blood relationship, but most families would refer to them as a cousin.
The granddaughter is the niece's first cousin once removed.