God's unchanging nature is something fundamental in scripture, before there ever was a church council or New Testament tradition. It is not based on a Greek concept of perfection but a biblical concept of God.

For I the Lord do not change (ESV, Malachi 3:6)

To ask when it first showed up in church father writings would probably be the same as asking when the first record of the subject has been preserved in what little literature we have from that time.

Before St. Augustine God was already spoken of as immutable, but St. Augustine, speaking more frequently than others about God's nature, refers to His immutability frequently. Here is a sample:

Thus, there can be no unchangeable good except our one, true, and blessed God. All things which He has made are good because made by Him, but they are subject to change because they were made, not out of Him, but out of nothing. Although they are not supremely good, since God is a greater good than they, these mutable things are, none the less, highly good by reason of their capacity for union with and, therefore, beatitude in the Immutable Good which is so completely their good that, without this good, misery is inevitable. (St. Augustine, City of God 12.1)

The first recorded reference of God's immutability in the Christian church, aside from those in scripture itself, may be Aristides of Athens; his Apology, Section IV (AD 125) mentions it.

It is the traditional Hebrew view of God's absolute unity necessarily implies His immutability and from this standpoint the end of the law under the new covenant has often been a stumbling block to them. I only point out that the unchangeable nature of God is not based on Greek concepts but Hebrew and then Christian concepts from scripture.

Every good gift and every perfect gift is from above, coming down from the Father of lights with whom there is no variation or shadow due to change. (ESV, James 1:17)

Writings

Very early. At least as early as Justin Martyr, in The First Apology (~AD 150):

For they proclaim our madness to consist in this, that we give to a crucified man a place second to the unchangeable and eternal God, the Creator of all; for they do not discern the mystery that is herein, to which, as we make it plain to you, we pray you to give heed.

Theophilus of Antioch, in Book I of his writings to Autolycus (~AD 170–80):

And He is without beginning, because He is unbegotten; and He is unchangeable, because He is immortal.

Also, Tertullian, in Against Hermogenes (~AD 200):

[B]eing the Lord, He is indivisible, and unchangeable, and always the same.

Origen, around AD 235, wrote On Prayer, in which he writes:

But in the case of God, inasmuch as He is himself ever unchangeable and unalterable, the proper name which even He may be said to bear is ever one, that mentioned in Exodus, "He that is," or the like.

Creeds

With respect to creeds, the AD 325 version of the Nicene Creed specifically mentions the immutability of the second person of the Trinity:

But those who say: [...] 'The Son of God is created,' or 'changeable,' or 'alterable'— they are condemned by the holy catholic and apostolic Church.

The Chalcedonian Definition (AD 451) says something similar.

Considerations

When considering this question, we need to remember that:

1. We don't have much in the way of early writings of the church (i.e., 2nd century)
2. Early creeds were not meant to nail down every point of Christian doctrine: they were often written as responses to particular heresies, and if no heretical group challenged the immutability of God, then that phrase would be unlikely to occur in a creed.

The fact that the immutability of God is so well attested in Scripture (in addition to the excellent verses mentioned in Mike's answer, we have Exodus 3:14, Psalm 102:26–28 and Hebrews 1:11–12, among others), it seems likely that no one seriously challenged this doctrine in the early church, except in the case of Christ's nature. Therefore, there was no need to make more than passing reference to it in writings, and no need to include mention of it in the creeds.