Your child's grandparents may take you to court to try to force visitation. If there is a reason why your child should not visit with a grandparent, by all means raise the issue in court. But make sure the reason is one affecting your child's life and not your own needs, pride, or anger.
If there's no valid reason a court would protect the children from the grandparents, it's likely that the grandparents will receive some form of visitation, especially if a prior healthy relationship existed between the grandparents and your children. So, if you have to appear in court, it's best to arrive with a proposed visitation schedule in hand. It's better to have your own wishes enforced than to have a judge set the schedule.
It's reasonable to offer between one and three afternoons a month, for a few hours at a time. This could be for lunch and a movie or a play session at the local park. If you and your child don't know the grandparents very well, you can ask the court to allow visitation to occur in your presence. If the grandparents live in another state, visitation over an entire weekend may be considered.
However, before you end up in court, try to reach a solution that works for all of you. You may find that spending a few hundred dollars to hire a mediator (neutral third party) to help you reach a visitation agreement is money well spent.