If you want less of something, tax it. How about a "for the children" "emergency wartime" tax on divorce falling on the party who files for it? The more confiscatory the levy, the fewer divorces you will see. I guarantee it.
You might say that this would just cause people not to marry. If you want more of something, subsidize it. The government can use some of the proceeds from the divorce tax to pay marriage bonuses.
I realize none of this will ever happen.
The divestiture of the current gyncentricized and virtually immutable child-custody advantage would be the single most powerful tool for dramatically decreasing the divorce rate here in the United States of America.