Q: Can a Christian be demon-possessed?
A: Absolutely not. First Corinthians 6:19 declares that the body of the Christian is the temple of the Holy Spirit. That is to say, Scripture makes it clear that believers are indwelt by God: the Father, Son, and Holy Spirit (John 14:17, 23). To conclude, therefore, that Christians can be demonized is to admit that demons can inhabit the very temple of God Almighty.
This is indeed difficult to believe, given Jesus' insights on possession: "When a strong man, fully armed, guards his own house, his possessions are safe. But when someone stronger attacks and overpowers him, he takes away the armor in which the man trusted and divides up the spoils" (Luke 11:21-22). Clearly, the "strong man" who guards Christians is the sovereign God Who created and sustains the heavens and the earth, Who is unable to be overpowered or plundered (2 Chr. 20:6).
Nevertheless, we must realize that our warfare is not against flesh and blood, but rather, against principalities and powers of darkness (Eph. 6:12). That is precisely why we are exhorted to put on the full armor of God (Eph. 6:11). However, we can say with confidence that Christ has already won the victory and no Christian can be "demon-possessed" (Col. 2:15). As God's Word triumphantly proclaims, "Greater is He that is in you, than he that is in the world" (1 John 4:4b).