Your first cousin's child and your child are second cosins.
Your first cousin's grandshild and your child are second cousins, once removed.
Your second cousin's child and your child are third cousins.
Your second cousin's grandchild and your child are third cousins, once removed.
his cousin
You and your uncle's grandson are first cousins once removed.
Your niece's child and your grandson's child (your great grandchild) are second cousins, once removed, to each other.
The grandchildren of siblings are second cousins to each other.
Your grandson and your great nephew are second cousins to each other.
Your sister's child and your grandson are first cousins once removed.
You and your first cousin's grandson are first cousins, twice removed, to each other.
Your grandson and great grand son could be cousins,(first cousins once removed), they could be uncle and nephew, or they could be father and son. It depends on how they are related to your children. If your great grandson is the grandchild on one of your children and your grandson is the child of a different one of your children, they are first cousins, once removed. If your great grandson is the child of a sibling of your grandson, then they are uncle and nephew. But your great grandson could also be the son of your grandson. Then they are father and son
You and your great aunt's grandson are second cousins. Your great aunt was the sibling of one of your grand parents, so your parent and your great aunt's child were first cousins. You and the grandson are members of the next generation and therefore second cousins.
Your child and your niece are first cousins to each other. Your child and your niece's child are first cousins, once removed.
Your child and your nephew are first cousins. Your child and your great nephew are first cousins, once removed.
Your uncle's granddaughter and your child are second cousins.
First cousin once removed.