Your cousin (if a first cousin) and your child are first cousins once removed.
Assuming both children are on the same side of the family, your child's first cousin is a second cousin to your first cousin's child. Your child is also a second cousin to your first cousin's child. Your child can have first cousins who are not related to your first cousin and thus not related to your first cousin's child.
Of course, your first cousin's child is related to you; you have ancestors who are also ancestors of your cousin's child. Your first cousin's child is your first cousin, once removed. Your second cousin's child is your second cousin, once removed.
Your second cousin's child is your second cousin, once removed.
The child of your father's first cousin is your second cousin.
Your cousin's child would be your first cousin once removed. So, your cousin's adopted child would be your adopted first cousin once removed?
Your first cousin's child is your first cousin's, once removed. Your second cousin's child is your second cousin, once removed. Your third cousin's child is your third cousin, once removed.
Your first cousin's child is your child's second cousin. Your second cousin's child is your child's third cousin. Your third cousin's child is your child's fourth cousin. and so forth
Your second cousin and your child are second cousins, once removed.
Your second cousin and your child are second cousins, once removed.
The child of your First Cousin, and you are First Cousin's, Once Removed.
You and the child of your first cousin are first cousins once removed.You and your first cousin's child are first cousins, once removed, to each other.
Your child and your first cousin are first cousins, once removed to each other.