Petition for (Custody) (Visitation). These forms and instructions are available in the General Clerk's Office, Room 108, in the Nassau County.To be successful, a Grandparent Visitation Petition is written as a two step process. A grandparent must show that visitation is in the child's best interests. When Can Grandparents File for Visitation Rights? Grandparents are eligible to file for visitation rights under specific circumstances once every two years. Grandparents can file a petition for visitation rights only when it serves the best interests of the child. Each of the documents listed below inculde a blank form and the instructions to fill out that form.