I recently watched a video series on the life of St. Teresa of the Andes. One of her older brothers was going seriously astray – staying out partying until all hours, alcohol, women, the works. Teresa (known to her family as Juanita) stayed up late until he came home, not so she could preach to him, but so she could serve him for the love of God.
St. Francis of Assisi is credited as telling his brothers to preach constantly, and if necessary, to use words. His point was that their actions must preach the gospel.
My point, if I can make one today, is that the best way to evangelize to anyone, is most likely through loving service, performed for the love the Christ. If you love your father to the best of your ability, and “put your love into living action” (as Blessed Mother Teresa used to say), you will be providing a powerful witness to the Truth.
If God wants you to speak, He will open that door and put the words into your mouth. In the meantime, pray and make sacrifices for his conversion. The prayers of a child for his/her father are precious to Christ.
Incidentally, my son’s dad is also not a Christian, but even though this man is my peer (same age, education level, etc.) I feel fairly certain that I am not to talk to him about God at this point. The evangelizing God wants of me in this case is to love this man unconditionally (not an easy task with an ex-husband!) and to look for opportunities to be of service to him.
I will be praying for your family!