The child of your father's first cousin is your second cousin.
Your cousins child is your first cousin once removed.
Your child and your first cousin's child are second cousins. Your child and your second cousin's child are third cousins to each other.
Your first-cousin and your child are first cousins, once removed.
Your child and your sister's daughter are first cousins. Your grand child and your sister's daughter are first cousins, once removed.
A child of two first cousins is the child of the parents and they are the child's mother and father. As the child of one first cousin, the child is also the first cousin, once removed, of the other parent. That, however, is of no importance. The closer relationship of parent and child is the one that really matters.
Your son and your 1st cousin's child are 2nd cousins.
Your sister's child and your grandson are first cousins once removed.
Your son and your aunt's child are first cousins, so your son and your aunts grandson (the son of your aunt's child) are first cousins, once removed.
The relationship between your sister's (or brother's) child and your cousin is the same as the relationship between your child and your cousin. Your child and your first cousin are first cousins, once removed. Your child and your second cousin are second cousins, once removed, and so forth.
First cousins once removed. Your child and your nephew are first cousins and there is one generation difference.
it's your first cousin, once removed
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.