For an atheist to be a God parent they will have to lie about their intentions and their beliefs.
The questions the priest asks the parents and Godparents in the C of E service are:
Priest: Parents and godparents, the Church receives these children with joy. Today we are trusting God for their growth in faith. Will you pray for them, draw them by your example into the community of faith and walk with them in the way of Christ?
Parents and Godparents: With the help of God, we will.
Priest: In baptism these children begin their journey in faith. You speak for them today. Will you care for them, and help them to take their place within the life and worship of Christ’s Church?
Parents and Godparents: With the help of God, we will.
In another part of the service there is a profession of faith. The parents and Godparents are expected to make this statement or a similar one.
Priest Let us affirm, together with these who are being baptized, our common faith in Jesus Christ.
Do you believe and trust in God the Father, source of all being and life, the one for whom we exist?
Reply I believe and trust in him.
Priest Do you believe and trust in God the Son, who took our human nature, died for us and rose again?
Reply: I believe and trust in him.
Priest: Do you believe and trust in God the Holy Spirit, who gives life to the people of God and makes Christ known in the world?
Reply I believe and trust in him.
This is the faith of the Church.
We believe and trust in one God,
Father, Son and Holy Spirit.
Not much wriggle room there is you are an atheist.