"How does it appear that children have a right to baptism?
"Children are parties in the covenant of grace. The covenant was made with them. 'I will establish My covenant between Me and you, and your seed after you, for an everlasting covenant, to be a God unto you, and to your seed after you,' (Gen. 17:7). 'The promise is to you and to your children,' (Acts 2:39). The covenant of grace may be considered either, (1) More strictly, as an absolute promise to give saving grace; and so none but the elect are in covenant with God. Or, (2) More largely, as a covenant containing in it many outward glorious privileges, in which respects the children of believers do belong to the covenant of grace.
"The promise is to you and to your seed. The infant seed of believers may as well lay a claim to the covenant of grace as their parents; and having a right to the covenant, they cannot justly be denied baptism, which is its seal. It is certain the children of believers were once visibly in covenant with God, and received the seal of their admission into the church; where now do we find this covenant interest, or church membership of infants, repealed or made void? Certainly Jesus Christ did not come to put believers and their children into a worse condition than they were in before. If the children of believers should not be baptised, they are in worse condition now than they were in before Christ's coming."