How would you help a spiritually stagnant church?
I would begin by preaching the gospel and displaying the infinite and all-satisfying worth of God. In other words, I wouldn't start at the symptom. Absence of love is a symptom of the absence of faith. And absence of faith is a symptom of the absence of seeing the beauty of God. It's the absence of truth.
You need to start at the bottom and just celebrate the glory of God—especially near the cross, because these people are going to need forgiveness. After that you move on to seeing the beauty of the cross. Then you work on being satisfied with and savoring the beauty of the cross. Finally you come to all of the fruits that begin to grow out of a happy church.
My goal in fixing the love problem is to fix the prior-satisfaction problem. The reason people aren't loving each other is because they think that satisfaction is found only in having the last word in arguments, revenge, or personal securities (which keep them people getting out of their comfort zone in order to bless other people). But all such satisfactions are lies of sin. They lie and say that more satisfaction is to be found in unloving ways than by going back to Jesus, finding complete satisfaction in him, and letting that spill over onto others, even if it costs you something.
You must start with what will make people happy in God, namely, a display of the beauty and the glory of God.