There are several basic types of visitation schedules that are most common among unmarried parents. The schedules are dependent on the level of the anticipated cooperation between the parents, and the desired level of specification requested in the visitation schedule.
If you are looking for a flexible schedule, and the custodial and non-custodial parent are able to get along, you can keep the schedule simple and flexible by agreeing that visitation will take place as the parties agree. The problem with this schedule is that you may wind up in Court again to set a specific schedule because one of the parties refuses to agree.
If the custodial and non-custodial parent are not able to get along, or if the parents would rather have a set schedule to avoid conflict, they may want to set a specific visitation schedule. A common schedule is for the non-custodial parent to have custodial access on alternating weekends from Friday evening through Sunday evening, a weeknight for a few hours every week, alternate major holidays, split the child's winter and spring breaks from school, and each party to receive two to four uninterrupted weeks in the summer, fathers day, and mothers day. The problem with this schedule is the lack of flexibility, however, the schedule can be virtually anything that the parties agree, and as flexible as the parties wish.
If parents live far apart and regular weekend visitation is not practical, it is common to allocate more summer vacation and school holidays to the non-custodial parent so that the child will spend substantial uninterrupted time with the non-custodial parent.
If the non-custodial parent is unstable, or addicted to alcohol or drugs, or has abused or neglected the children, then you may want to request that the non-custodial parent have supervised visitation. Although you are likely to encounter resistance when you propose such a schedule, perhaps you can craft some type schedule that has other safeguards just short of supervised that may be agreeable to the non-custodial parent, or seek a hearing on the matter.
In New York, grandparents may have a legal right to visitation in certain circumstances. In order to prevail the grandparent must show that 1) they have legal standing, and 2) granting visitation rights is in the best interest of the child. Generally, grandparents will be found to have legal standing if one of the parents of the child is deceased, or that circumstances exist that make it proper for the Court to intercede because the parents object to the visitation, and the grandparents have a sufficient existing relationship with the child or have at least made a sufficient effort to establish one.