Your cousin's son would be your nephew. If he or she had a daughter, then she would be your niece. The same would apply to you if you had any children of your own. This would also be the case when referring to children of your brothers or sisters.
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Your cousin's son is basically your second cousin. It is however, okay for them to refer to you as their aunt or uncle if there is a significant age difference. Most people find it confusing when it comes to identifying second and third cousins.
John Fitzgerald Kennedy, Jr. (November 25, 1960 – July 16, 1999), often referred to as JFK Jr. or John-John in the press, was an American lawyer, journalist, and magazine publisher. He was the son of ...