At what age can a child refuse visitation with the non-custodial parent in Illinois? And if a child can refuse visitation, what reasons are acceptable?
What makes you think it's EVER OK for a minor child to refuse visitation with NCP? (HINT: Unless there is irrefutable evidence of physical abuse or neglect, there shouldn't be a good reason for it. If you suspect that the child is being abused by the NCP, then you need to get Children's Services involved.)
If the child is simply not wanting to visit for their own personal reasons, then that isn't good enough. And YOU have no business even giving them a reason to think that it's OK not to visit with the NCP.
It's NOT your job to allow your child to dictate his choices here. The court already did that for you. It IS your job as the CP to encourage and facilitate the relationship between the child and NCP. The court granted them visitation rights, and you are not legally in a position to challenge the court's decision here. If you try to withhold the visitations simply because the child does not want to go, you can still be held in contempt if NCP decides they want to pursue it.
If there is difficulty in the relationship between NCP and the child, then I would suggest you seek counseling for the child to help them cope with their issues, because NOT sending them to the visits is NOT an option here for you.