Paidion is correct. God not only feels pain but rejoices. According to the Christian philosopher Alvin Plantinga:
Now a widely shared traditional view of God has been that he is impassible, without desire or feeling or passion, unable to feel sorrow at the sad condition of his world and the suffering of his children, and equally unable to feel joy, delight, longing, or yearning. The reason for so thinking, roughly, is that in the tradition originating in Greek philosophy, passions were thought of (naturally enough) as passive, something that happens to you, something you undergo, rather than something you actively do. You are subject to anger, love, joy, and all the rest. God, however, is pure act; he doesn’t ‘undergo’ anything at all; he acts, and is never merely passive; and he isn’t subject to anything. As far as eros is concerned, furthermore, there is an additional reason for thinking that it isn’t part of God’s life: longing and yearning signify need and incompleteness. One who yearns for something doesn’t yet have it, and needs it, or at any rate thinks he needs it; God is of course paradigmatically complete and needs nothing beyond himself. How, then, could he be subject to eros? God’s love, according to this tradition, is exclusively agape, benevolence, a completely other-regarding, magnanimous love in which there is mercy but no element of desire. God loves us, but there is nothing we can do for him; he wishes nothing from us.
On this particular point I think we must take leave of the tradition; this is one of those places where it has paid too much attention to Greek philosophy and too little to the Bible. I believe God can and does suffer; his capacity for suffering exceeds ours in the same measure that his knowledge exceeds ours. Christ’s suffering was no charade; he was prepared to endure the agonies of the cross and of hell itself (“My God, my God, why have you forsaken me?”). God the Father was prepared to endure the anguish of seeing his Son, the second person of the trinity, consigned to the bitterly cruel and shameful death of the cross. And isn’t the same true for other passions? “There is more rejoicing in heaven over one sinner who repents than over ninety-nine righteous persons who do not need to repent” (Luke 15:7); is God himself to be excluded from this rejoicing?
Similarly for eros: “As a bridegroom rejoices over his bride, so will your God rejoice over you” (Isaiah 62:5). The bridegroom rejoicing over his bride doesn’t love her with a merely agapeic love. He isn’t like her benevolent elder brother (although Christ is also said to be our elder brother). He desires and longs for something outside himself, namely union with his beloved. The church is the bride of Christ, not his little sister. He is not her benevolent elder brother, but her husband, lover. These scriptural images imply that God isn’t impassive, and that his love for us is not exclusively agapeic. They suggest that God’s love for his people involves an erotic element of desire: he desires the right kind of response from us, and union with us, just as we desire union with him. ~~ Warranted Christian Belief (online)