I think on some level the difficulty has come from the fact that, in the history of Christianity there has been two competing notions of the divine. One based upon philosophy, and one based upon theology.
The philosophical view begins with a set of abstract ideas--God is omnipotent, God is X, God is Y. What we would describe as the "attributes of God".
But I think the appropriate position to take is the theological one, not the philosophical one. It's the position that Martin Luther takes in the Heidelberg Disputations about what it means to be a theologian of the cross. And that doesn't begin with abstract ideas, the attributes of God; rather it begins with the concrete, solid, person of Jesus who lived, suffered, died, and rose again.
Hence Luther writes,
"19. That person does not deserve to be called a theologian who looks upon the »invisible« things of God as though they were clearly »perceptible in those things which have actually happened« (Rom. 1:20; cf. 1 Cor 1:21-25).
This is apparent in the example of those who were »theologians« and still were called »fools« by the Apostle in Rom. 1:22. Furthermore, the invisible things of God are virtue, godliness, wisdom, justice, goodness, and so forth. The recognition of all these things does not make one worthy or wise.
20. He deserves to be called a theologian, however, who comprehends the visible and manifest things of God seen through suffering and the cross.
The manifest and visible things of God are placed in opposition to the invisible, namely, his human nature, weakness, foolishness. The Apostle in 1 Cor. 1:25 calls them the weakness and folly of God. Because men misused the knowledge of God through works, God wished again to be recognized in suffering, and to condemn »wisdom concerning invisible things« by means of »wisdom concerning visible things«, so that those who did not honor God as manifested in his works should honor him as he is hidden in his suffering (absconditum in passionibus). As the Apostle says in 1 Cor. 1:21, »For since, in the wisdom of God, the world did not know God through wisdom, it pleased God through the folly of what we preach to save those who believe.« Now it is not sufficient for anyone, and it does him no good to recognize God in his glory and majesty, unless he recognizes him in the humility and shame of the cross. Thus God destroys the wisdom of the wise, as Isa. 45:15 says, »Truly, thou art a God who hidest thyself.«
So, also, in John 14:8, where Philip spoke according to the theology of glory: »Show us the Father.« Christ forthwith set aside his flighty thought about seeing God elsewhere and led him to himself, saying, »Philip, he who has seen me has seen the Father« (John 14:9). For this reason true theology and recognition of God are in the crucified Christ, as it is also stated in John 10 (John 14:6) »No one comes to the Father, but by me.« »I am the door« (John 10:9), and so forth." - Martin Luther, Heidelberg Disputation, Theses 19-20
Thus we behold God not through the invisible and abstract notions of power, wisdom, glory, et al; but rather through the visible and tangible reality of the Crucified Jesus. And thus we behold God not in wisdom, but foolishness; not in power, but weakness; not in glory, but the cross.
And so the definition of "divine" is found not through abstract and invisible notions of attributes; but instead in God's acts, God's self-pouring-forth, God's self-giving, etc.
I've always loved the following quote from the Catholic theologian Fr. Herbert McCabe
"This is what John is talking about at the beginning of his Gospel when he calls Jesus the Word of God made flesh. Jesus is God's Word, God's idea of God, how God understands himself. He is how-God-understands-himself become a part of our human history, become human, become the first really thoroughly human part of our history--and therefore, of course, the one hated, despised, and destroyed by the rest of us, who wouldn't mind being divine but are very frightened of being human." - Herbert McCabe, God Still Matters, p104
And of course it is only this Incarnational understanding of God that can make sense of the multifaceted dimensions of Christian theology; perhaps no more so noticeable than in the doctrine of Theosis. So when St. Athanasius declares, "He became man so that man might become god." this can only be understood through the Incarnation; for the great doctor does not mean we become "almighty" or "eternal" or any of these attributes; but rather speaks of our sharing in God through Jesus and the Spirit. We don't become "gods" by some form of apotheosis; but rather that ultimately and in the end God's grace utterly penetrates us through the transformative and transfigurating work of the Spirit conforming us to the image of Christ. This work which shall be made full and perfect in the resurrection.
God, and so divinity, cannot be comprehended in any other way, at least not honestly, except through Jesus who gives Himself freely in suffering, death, and life.
And so what is divine is That which we encounter in the weakness, humility, and grace of Jesus Christ.
-CryptoLutheran