God the Son
This is found in Athenagorus's A Plea for the Christians, chapter ten: "The Christians Worship the Father, Son, and Holy Ghost." The year was ad 177. Not too long after that, we find the phrase in Clement of Alexandria. He mentions the "Blood of God the Son" in The Salvation of the Rich Man. Later references were made by Tertullian, Novatian (in arguments against the modalists), and others.
God the Holv Spirit
There is not a mention of this term (or "God the Holy Ghost") in the early patristic era. In the early 400s, Augustine, in his On the Holy Trinity (Book 15, Chapter 17,"How the Holy Spirit is Called, Love, and Whether He alone is so Called..."), writes:
But they have said, "God is love," so that it is uncertain and remains to be inquired whether God the Father is love, or God the Son, or God the Holy Ghost, or the Trinity itself which is God.
Clement of Alexandria (c. 150-215) first used this term in the Exhortation to the Heathen, chapter 12. Later this phrase was in the "Liturgy of the Blessed Apostles," by St. Adaeus and St. Maris, "Teachers of the Easterns":
Holy art Thou, O God our Father, truly the only one, of whom the whole family in heaven and hearth is named. Holy art Thou, Eternal Son, through whom all things were made. Holy art Thou, Holy, Eternal Spirit, through whom all things are sanctified.
Further, we find frequent use of the term in Augustine's On the Holy Trinity. Also, in his Lectures on the Gospel According to St. John (Tractate 21), Augustine wrote:
For He is the Son equal to the Father, the eternal Son with the Father, and co-eternal with the Father, but we became sons through the Son, adopted through the Only-begotten.
We find no use of the term "co-equal" in the earlier patristic documents, even though the Cappadocians and the Council of Constantinople propagated the theology with different words. In a short time later, though, Augustine used the term in his book On the Holy Trinity:
The Father hath begotten the Son, and so He who is the Father is not the Son; and the Son is begotten by the Father, and so He who is the Son is not the Father; and the Holy Spirit is neither the Father nor the Son, but only the Spirit of the Father and of the Son, Himself also co-equal with the Father and the Son, and pertaining to the unity of the Trinity.
We first find a mention of this in The Extant Works and Fragments of Hippolytus (ad 170-236), not with the typical later trinitarian definition of the Son, but nonetheless used:
Thou Friend of man, when saw we Thee sick or in prison, and came unto Thee? Thou art the ever-living One. Thou art without beginning, like the Father, and co-eternal with the Spirit. Thou art He who made all things out of nothing. Thou art the prince of the angels. Thou art He at whom the depths tremble. Thou art He who is covered with light as with a garment. Thou art He who made us, and fashioned us of earth. Thou art He who formed things invisible. From Thy presence the whole earth fleeth away.
Later this term and the others were used much in Augustine's writings, such as On the Trinity. Here is a sample from another of his writings, Instructing the Unlearned:
For this same Christ, the only-begotten Son of God, the Word of the Father, equal and co-eternal with the Father, by whom all things were made,was Himself also made man for our sakes, in order that of the whole Church, as of His whole body, He might be the Head.
It is amazing that these labels were absent not only from the Scriptures but also from the first one hundred years of the church's history. Why should we look upon them today as orthodox?