Sharing the Gospel with a friend who doesn't believe in God need not be a difficult thing to do. This is because Christ Himself showed us how to do it:
By loving people unto God.
The Lord Jesus Christ, the very person we preach to others, is very loving. He is actually the kind of person that everyone wants to have as a friend, a lover, a brother, a colleague, a mentor. He's who Haggai 2:7 tells us:
"...the Desire of All Nations..."
While religious teachings drive people away, true and unbiased presentations of Christ will draw all people to Him. He is very, very desirable, and the multitudes of people who followed Him during His earthly ministry are proof of that.
That said, there are many, many things in the Bible that we can and should share with our non-believing friends. The Word of God contains wisdom for any and everything that pertains to life, and it is a treasure trove full of God's instruction, warning, comfort, and encouragement to all who run to Him.
Yes, it's also full of loving invitations to those who don't know Him.
With that, here are a few Bible verses you can and should share to your non-believing friends. All of these will draw them near to Him, if we share them with our friends.
"I am the door. If anyone enters by Me, he will be saved, and will go in and out and find pasture. The thief does not come except to steal, and to kill, and to destroy. I have come that they may have life, and that they may have it more abundantly."
"For the wages of sin is death, but the gift of God is eternal life in Christ Jesus our Lord."
"For I know the thoughts that I think toward you, says the Lord, thoughts of peace and not of evil, to give you a future and a hope. Then you will call upon Me and go and pray to Me, and I will listen to you. And you will seek Me and find Me, when you search for Me with all your heart."
"Let us hear the conclusion of the whole matter: Fear God and keep His commandmentsfor this is man's all. For God will bring every work into judgment, including every secret thing, whether good or evil."
"For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. For God did not send His Son into the world to condemn the world, but that the world through Him might be saved. He who believes in Him is not condemned; but he who does not believe is condemned already, because he has not believed in the name of the only begotten Son of God."