What is the name for my relationship with my child's spouse's cousin (child-in-law's cousin) (daughter's husband's cousin) (son-in-law's cousin)?
To know your relation to x, consider what the relationship of your corresponding person, on the in-laws side has with x.
Here, the corresponding person would be your child's spouse's father. He is an uncle to the cousin. Hence, the given cousin is your nephew-in-law (or niece-in-law)