One approach, of course, would be to ask him to show you a contradiction in the Bible. Most people like this can't do it; they've actually never read the Bible, and are only repeating what they've heard someone else say about it.
But this might only embarrass or anger your uncle -- and that shouldn't be your goal. Instead, your goal should be to make him face his need of Christ. After all, your uncle's scorn for the Bible is only an excuse -- an excuse for avoiding God. He may not even realize what he's doing -- but by saying the Bible can't be trusted, he's refusing to face his own need of God, and refusing also to accept the Bible's claim that God loves him.
Pray for your uncle; only God can open his heart and convince him of the truth of the Gospel. Pray too that nothing -- his pride, or his desire to run his own life, or his attachment to some particular sin, or anything else -- will keep him from facing his need for God's forgiveness and grace.
In addition, ask God to help you be a witness to your uncle, both by your life and your words. Don't argue with him, but let him know you care for him, and urge him to face the reasons why he doesn't want anything to do with God. The Bible says, "Let your conversation be always full of grace, seasoned with salt, so that you may know how to answer everyone" (Colossians 4:6).