It goes like this: "If God can do anything, He can create a stone too heavu for Him to lift. If there's a stone too heavy for God to lift, He can't do everything. Therefore, there is no God."
Any logician will tell you that this formal argument is airtight. Its form makes it "valid" and irrefutable.
Of course, one problem with the argument from a believer's perspective is that it presumes the conditions by which God can "prove" His existence to us. If you are trying to prove or disprove the existence of the creator and Lord of the universe, it's presumptuous to define the parameters by which you'll allow Him to prove Himself to you.
God's preferred method of "proving" Himself and His love to us is through self-disclosure, the persuasions of the Holy Spirit, and the gift of faith. Each of these methods, resulting in faith, are initiated by God. Hard as it is on human egos, theists believe no one can every be argued into or out of faith by valid arguments.
But, for the moment, let's accept that both assertions of the "parable" are true:
1. God can do anything.Are the two parts mutually exclusive? If you say, "Yes" to #1 and "Yes" to #2 or "No" to either proposition, are you conceding that God doesn't exist?
2. God can create a stone too heavy for God to lift.
Actually, I don't think so.
As a Christian, I accept that God can do anything. But I also accept that this God Who can do anything can create a stone too heavy for Him to lift. And yet, I conclude that God exists.
This is exactly what happened when God took on human flesh in the person of Jesus, submitting to the limitations of being human (even while totally resisting sin) and presumably, during His time on earth, encountering stones that would have been too heavy for Him to lift had He tried. (He could have caused them to cry out, by the way. But that's another story.)
Of course, all supposedly airtight arguments against God's existence have, for the person willing to receive the witness of Scripture and of Christ's Church and so, being willing to believe in Christ, been trumped by Jesus' life, death, and resurrection.
In Jesus Christ, we meet the eternal and infinite God, able to do anything, including incorporate the experience of human weakness into the experience of Almighty God.
In Jesus Christ, we meet the compassionate God Who voluntarily lived with human weakness and limitation to win us back through the submission of His weak body to death.
Those who let Jesus into their lives don't need a counter-argument to the parable of the stone. The crucified and risen Jesus is evidence of the God Who can do anything, including carrying the weight of our sins on a cross and rising from the dead from a tomb once sealed by a stone too big for one person to budge.
God is mighty. God is vulnerable. Therefore God exists. And, therefore, He and He alone can give life to all who believe in Jesus Christ!