You probably won't be able to argue an Atheist into believing in God. When I was an Atheist, I laughed at the arguments which Christians presented to me, because I had heard them all before and had answers for them already. But secretly, in my heart, I wept because I WANTED them to give me an argument that I couldn't answer. No one ever did.
And yet .. today I am back in the Catholic Church! Why? Well, it wasn't because a Christian gave me an airtight "proof for God" that I couldn't argue against. It was simply because a Christian was kind to me, and shared a joke with me that made me laugh -- and treated me as a friend rather than an enemy.
Let me tell you a (not so hidden!) secret - most of the Atheists you meet online think that all Christians are stupid. Really, they think we are intellectually inferior to them. So at best, the Atheists will treat us patronizingly -- "poor things, they just don't know any better" - and at worst, with scorn and contempt -- "idiots - how can anyone live that way?" (And by the way, don't quote that psalm about how "The fool says in his heart, there is no God" -- you are just confirming their belief that Christians hate them.)
You will have to mount a "sneak attack" to get past their armor - not by a full frontal assault, but by little "sorties". Humor is the BEST way. Not mean-spirited humor that makes fun of Atheists - that's just playing into their hands. Just gentle humor, intelligent humor - not even necessarily religious humor. Just get them to laugh with you - just once - and you are halfway home.
Be their friend. Love them. Pray for them (but don't tell them you're doing that!). Try to see them as individuals who, like each one of us, is in need of God's love and mercy. Atheists like to put up a bold front ("I can get along without 'god' just fine!"), but deep down inside, so deep that sometimes even they don't know it, there's a frightened little child, lost in the dark, looking for a ray of light.