Surely the timing is a miracle of God, but perhaps not in the way you seem to be implying. Psalm 83 is a prayer to vanquish the enemies of Israel, but we are focused on the Israel we see, a country surrounded by enemies that have opposed their occupation of that land, ever since the country was established, post WW II.
The Chief Rabbinate calling for prayer on behalf of Israel at this time, using Psalm 83, is a plea to God to defeat Hezbollah. The country, Israel, wants to completely eliminate its enemy. But we do not know what is meant by Israel and its enemies. The twelve tribes of Israel as mentioned Biblically are scattered throughout the world, and this could include current Muslims, Christians, Jews, and others. God may not mean for us to pray for the country Israel so much as to learn what He means by His "enemies."
Perhaps more aligned with the heart of Christ, try praying Psalm 85:8 -13. Israel, Lebanon, and Syria all need prayer.