This is an excellent practical resource from Covenant Life Church in Gaithersburg Md. (my old stomping grounds!) regarding ordinances (sacraments) and children. Must read!
In the earliest times of Christianity the ordinances held a very high place in the life of the church and the proper administration of them was of the highest concern. They were specifically related to one another and functioned as a defining feature of the nature of the church itself. As J. N. D. Kelly says: “From the beginning baptism was the universally accepted rite of admission to the Church; only ‘those who have been baptized in the Lord’s name’ may partake of the eucharist,” Early Christian Doctrines, p. 193.
During times of a revival of genuine New Testament Christianity, the importance of proper administration of the ordinances has always been revived among God’s people. John Bunyan and Jonathan Edwards are both good examples of this.
Church historian, Iain Murray comments on this pattern: “The same [revival] influence inevitably brought a return to biblical standards of church membership. It was no longer assumed that those who attended church from birth were Christians, nor was ‘profession of faith’ henceforth taken as sufficient evidence of conversion. Ministers and elders considered how people lived, and what they did, as well as what they said. It was understood afresh that the true usefulness of the church is bound up with her spirituality and her unity. The premature admission of young people to the Lord’s table (communicant membership), which had formerly been too common, now gave way to a more faithful examination of candidates.” Revival & Revivalism: The Making and Marring of American Evangelicalism 1750-1858, p. 106.