You have described a crime. Crimes should be reported to law enforcement. Although private citizens can sue one another, the usually do so when there has been damages that can be converted into money. Unless you are looking for money, there might not be much reason to sue another person. If you are looking for a Court to hold a person accountable for illegal behavior, that's what the criminal justice system does.
The short answer is yes, you can sue. You could file a suit claiming negligence, intentional infliction of emotional distress, etc. The real question is does the pervy cousin have assets worth the fight? If he owns a home, has a high-paying job, or there is some other asset which may be able to be seized; I would highly recommend the parents/guardians of the minor try to find an attorney who would be willing to represent them (the parents/guardians likely have a claim for the distress inflicted upon them due to the acts perpetrated upon their child). If the reprobate drives a Prius, lives in an apartment, and works in electronics at Best Buy; you would likely find it difficult to obtain counsel on a contingency fee basis.
