Irenaeus – Against Heresies 2.22.4:
“He came to save all through Himself, all I say, who through Him are reborn in God, infants, and children, and youth, and old men. Therefore He passed through every age, becoming infants for infants, sanctifying infants; a child for children, sanctifying those who are of that age, and at the same time becoming for them an example of piety, of righteousness, and of submission; a young man for youths, becoming an example for youths and sanctifying them for the Lord.”
Origen – Cited in Robert Rayburn, What About Baptism? (The Covenant College Press, 1957), 52:
“For what is sin? Could a child who has only just been born commit a sin? And yet he has sin for which it is commanded to offer a sacrifice, as Job 14:4ff and Psalm 51:5-7 show. For this reason the Church received from the Apostles the tradition to administer baptism to the children also. For the men to whom the secrets of divine mysteries had been entrusted knew that in everyone there were genuine defilements [sic], which had to be washed away with water and the Spirit.”
Cyprian – Letter 58 to a pastor named Fidus:
“1. Because God is no respecter of persons and his grace is universally given to all types, baptism ought to be administered to both adults and infants.
2. Because God is no respecter of persons and because his grace is universally given to all types, baptism ought to be given to adults and children and not limited to any particular age.
3. Because the grace of God is given to those who receive it in an equal measure, baptism ought to be given to both adults and children.
4. Since outward circumcision was abolished with the coming of Christ we are now given a “spiritual circumcision.”
5. Because God is no respecter of persons and because his grace is universally given to all types, baptism ought to be given to Jews and Gentiles alike: “spiritual circumcision ought not to be hindered by carnal circumcision.”
6. If grace and baptism is given to those who commit heinous sins, “how much rather ought we to shrink from hindering an infant, who, being lately born, has not sinned, except in that, being born after the flesh according to Adam, he has contracted the contagion of the ancient death at its earliest birth.”
Augustine – On Baptism, Against the Dentists, ed. Philip Schaff, in Nicene and Post-Nicene Fathers: Series 1 (reprinted; Peabody: Hendrickson, 2004), IV:461:
“And this is the firm tradition of the universal Church, in respect of the baptism of infants, who certainly are as yet unable “with the heart to believe unto righteousness, and with the mouth to make confession unto salvation,” as the thief could do; nay, who even, by crying and moaning when the mystery is performed upon them, raise their voices in opposition to the mysterious words, and yet no Christian will say that they are baptized to no purpose. And if any one seek for divine authority in this matter, though what is held by the whole Church, and that not as instituted by Councils, but as a matter of invariable custom, is rightly held to have been handed down by apostolical authority…”