Grandparent custody of a grandchild or grandchildren may be awarded under certain circumstances. However, there must be a compelling reason for grandparents to be awarded custody if either parent of the child is alive and capable of or interested in parenting the child.n some cases, a sibling or other blood relative may be awarded child custody. If there is a dispute over who will get custody of a child with deceased parents, the grandparents will have to prove to the court that it is in the child's best interest to live with them.