This is a brief summary of the David Engelsma's article three main views of how Presbyterians understand what it means for their children to be in the Covenant of Grace.
1) Jonathan Edwards and some Puritans held to this position. Baptized covenant children are in a privileged position and they are "covenant children" insofar as they are born into a Christian home and are more likely to be converted than children of non-Christians because they are more likely to hear the Gospel. Engelsma notes that it is the position of the Free Reformed Church of North America as well as the Netherlands Reformed Congregations of the United States and Canada.
2) All children of believers are in the Covenant of Grace. They are recipients of the covenant's promise but the fulfillment of this promise is conditional upon them coming to faith when they come of age. This is the view of both the American and Canadian Reformed Churches, as well as the Reformed Churches in the Netherlands.
3) Children are in the sphere of the covenant and receive its sign and seal, but only elect children are actually partakers of the Covenant of Grace. This is the position of the PRCA.