Can a court order that a child's time with grandparents come out of a specific parent's own parenting time?

Yes, this is actually a common way grandparent contact is structured in practice, particularly where the grandparent is connected to one parent's side of the family specifically. Rather than carving out separate time that comes from neither parent's schedule, a court can order that a grandparent's contact take place during that specific parent's own parenting time, on the reasoning that it's that parent's family connection being maintained, and it avoids reducing the other parent's own time with the child to accommodate it.

This approach tends to make practical sense and is often less contested than an arrangement that draws from both parents' time equally, especially where one parent supports the grandparent's contact and the other has no particular connection to that grandparent at all. That said, it isn't a rigid rule, and a court has flexibility to structure contact differently depending on the family's circumstances - for example, if the grandparent has an independent, strong relationship with the child that doesn't clearly track to one parent's time, or if practical scheduling makes another arrangement more workable. A family lawyer can advise on what structure makes the most sense given your specific family situation.