I must be alone to understand that since man failed to listen to God more than the female that both failed to be innocent, Therefore not being as lambs in spiritual dogma they must have been dressed with goat skins. A more coarse material than the softness of lamb skins. An irritating material which was why Moses said: The women who's heart stirred them up in wisdom spun goats hair. The dark color of sackcloth worn by men of God in penance was a reflection of the darkness of Adam and Eves heart when God banished them from Eden and they mourned in tears as they fled. Abraham conquered love for God and kept Gods command secret from his wife, his servants, and even his own son Isaac. Likewise Gods Ram substitute was a fully grown lamb which took the place of Isaac. Men of over sensual desires are called goatish in the dictionary because goats eat everything just like Adam wanted what was good fruit and fruit that made the heart void.
I have yet to find any satisfactory 'tradition' which adequately explains the absence of designation of the actual animal used by God in this instance. There is a lot of conjecture expressed about the matter but none that I have yet found to be accurate, only superstitious.
The traditions which I have found all attempt to improvise on what is not actually expressed by the scripture - and therefore miss the whole point of the allegory.
There is no information given in scripture as to the species which God used in order to clothe Adam and Eve with coats (kethoneth, long sleeved tunic, Strong 3801 ) of skins. It was an undefined species. The lack of information is highlighted by not being there.
Unto Adam also and to his wife did the LORD God make coats of skins, and clothed them. [Genesis 3:21, KJV.]
My own understanding of the lack of information is that what was to clothe humanity in the future did not - yet - exist. Therefore it could not - yet - be expressed. Therefore it is left un-defined in allegory.
That which clothes humanity unto righteousness is the humanity in which Christ came, as Head of a new humanity.
'Clothing' - the 'robe of righteousness' mentioned by the prophet Isaiah (61:10), and mentioned by the Apostle John in Revelation, the 'righteousnesses of the saints' being 'fine linen' (19:8) - is a matter of clothing the human soul with a new humanity, in righteousness.
For as in Adam all die, even so in Christ shall all be made alive. [I Corinthians 15:22, KJV.]
In order to be so clothed, in the 'skin' of Another, that 'other' must die, in sacrifice.
Do any Christian traditions exist as to what type of animal skin did God clothe Adam and Eve with?
The short answer is no.
Some individual Christians seem to believe that the skins may have been lambs or goats (sackcloth), etc. But that is a far as it goes.
That said there are some Christians and even Jews that think that before the fall Adam and Eve were clothed in light.
There are a number of people who believe that before Adam and Chava (Eve) sinned, they had bodies of light or bodies clothed with light, and that as a result of their sin, they lost their body/clothing of light. When examining the Hebrew language, this is not hard to see. - "Skins of Light and Flesh"
More can be seen here: Bereishit (5768) – The Garments of Light
Blessed Catherine Emmerich, in her revelations, tells us that they were also clothed in light before the fall.
[Adam and Eve] were like two unspeakably noble and beautiful children, perfectly luminous, and clothed with beams of light as with a veil. From Adam’s mouth I saw issuing a broad stream of glittering light, and upon his forehead an expression of great majesty. Around his mouth played a sunbeam, but there was none around Eve’s. I saw Adam’s heart very much the same as in the men of the present day, but his breast was surrounded by rays of light. In the middle of his heart, I saw a sparkling halo of glory. In it was a tiny figure as if holding something in its hand. I think it symbolized the Third Person of the Godhead. - Adam and Eve in the Writings of the Mystical Saints and Doctors of the Church
Immediately after the fall, Adam and Eve perceived that they were naked and sewed fig leaves together in order to hide their nakedness.
Then the eyes of both of them were opened, and they realized they were naked; so they sewed fig leaves together and made coverings for themselves. - Genesis 3:7
Later on we read that God made skins of animals for Adam and Eve to replace their fig leaves.
There is no Christian traditions as to what sort of animal these skins belonged to. However there is a Jewish tradition (amongst others) that the skins were from the very serpent that tempted our first parents.
However, the garment itself can be an object of transformation, not just a means for the wearer to transform the perceptions of others. In a midrash on the verses about Adam and Eve is this:
R. Eliezer said, "Of the skin that the serpent sloughed off God made coats of glory for Adam and his helpmeet; as it is said, ‘And God made for Adam and his wife coats of skin and He clothed them."(Gen 3:21) Pirke d’ rabbi Eliezer 20.
Avivah Zornberg writes of this midrash that its paradox is striking. The serpent, all deception, is reconstructed into an attribute of human dignity; the animal who brought temptation into the world can now, with his skin, be used as something with which to guard against temptation. - SNAKESKIN AND VEILS: GARMENTS IN GENESIS
And the Lord God commanded him, “You may eat freely from every tree of the garden, but you must not eat from the tree of the knowledge of good and evil; for in the day that you eat of it, you will surely die.” - Genesis 2:17
It seems the serpent paid the price as a reminder to Adam and Eve!