Did John Calvin believe that the grandchildren of a believer are entitled to infant baptism? In Calvinism, the children of believers are considered "members of the covenant" and as a sign of that covenant, they are baptized as infants.

Practically speaking, this means that if at least one parent is a Christian and member of the church, then the child may be baptized.  But sometimes, people other than the parents might be considered "responsible" for that child's spiritual well-being, and thus a child could be baptized even if neither parent is a Christian/church member.  

Sometimes those other people are grandparents, but the issue quickly gets tricky – for example, what about the cases of household slaves or foster children?  Usually, the litmus test is that the "sponsors" of the child must be in a situation to train and nurture the child.

However, I recently saw the claim that John Calvin believed that descendants of Christians, even several generations removed, were entitled to the sign of the covenant, without the requirement of a Christian "sponsor."  So, for example, the grandchild of a deceased member of the church would be entitled to infant baptism, even if no one else in the family is a Christian.

My initial reaction to this claim was skepticism, but on reflection I'm wondering if this would fit well within Calvin's system.  Did Calvin believe that descendants of church members, even to two or more generations, were entitled to infant baptism, even without a Christian guardian?  Where in his works does he argue for or against such a position?
John Knox, the leader of the Reformation in Scotland,  wrote to Calvin in 1559,  asking for his view on whether it be lawful to admit to the Sacrament of Baptism the children of idolators and excommunicated persons before their parents have testified their repentance.

In reply Calvin said he had consulted colleagues in Geneva and all were agreed.


  God's promise comprehends not only the offspring of every believer in the first line of descent, but extends to thousands of generations.


This is  a reference to the promise in the Second Commandment.

He went on:


  To us then it is by no means doubtful that an offspring descended from holy and pious ancestors, belong to the body of the Church,  though their fathers and grandfathers may have been apostates. 


and


  wherever the profession of Christianity has not been altogether interrupted or destroyed, children are defrauded of their privileges if they are excluded from the common symbol; because it is unjust, when God, 300 years ago or more, has thought them worthy of His adoption, that the subsequent impiety of some of their progenitors should interrupt the course of heavenly grace.


However he did insist suitable sponsors (godparents rather than guardians) were needed.


  We confess it is indispensible for them to have sponsors.


Dr Jules Bonnet, in the nineteenth century published a collection of Calvin's letters translated. This letter is letter 549.

Letters of John Calvin