State laws vary so you should see what legally your son, especially if he is a minor, and you, the parents, are responsible for before negotiating with the neighbors regarding the accident.
If you want to go through insurance to cover your child scratching another vehicle with his bicycle you will need to check and see if your homeowner's policy would cover this. Your auto insurance would not normally cover this since your vehicle was not used or involved in the incident.
The neighbor may go through their own car insurance if they have physical damage (collision coverage and comprehensive) as part of their car insurance policy on the vehicle. They would have to pay a deductible though, so you may be asked to cover this if state laws allow them to. Also since your son was at-fault their insurance company may be allowed to subrogate, which is to request that you to repay them for the claim they paid out where your son was the one who caused the damage.