No.
The daughter of your first cousin is your first cousin, once removed. The daughter of your second cousin is your second cousin, once removed. First cousins share grandparents. Second cousins share a great-grandparent; but not grandparents.
Your niece is the daughter of your brother or sister. Brothers and sisters share parents.
Your niece and your daughter are first cousins. Your niece's daughter and your daughter are first cousins, once removed.
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.
Your niece and your daughter are first cousins. Your daughter and the daughter of your niece are first Cousins, once removed.
Your daughter and your niece are first cousins. Your daughter than your niece's son are first cousin's once removed. Your daughter's child and your niece's child are second cousins to each other.
Your daughter and your niece are first cousins Your daughter and your great grand niece are first cousins, twice removed.
Your son and your niece are first cousins to each other. Your son and your niece's son are first cousins, once removed.
Your great great niece is the granddaughter of your niece or nephew. Your daughter and your niece or nephew are first cousins. Your daughter and your great great niece are first cousins, twice removed.
Your daughter and your niece are first cousins. Your daughter and your niece's daughter are first cousins, once removed.
Your daughter and your niece's daughter are first cousins, once removed.
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 niece and your daughter are first cousins to each other.
Your son and your niece are first cousins. Her daughter and your son are first cousins, once removed.