The good thing about your friend is that his faith is probably at an all-time high. The unfortunate thing is that he has been pumped up by those whose viewpoints are biblically suspect.
If your friend has been spending a lot of time under the influence of television faith healers then I can tell you right now your ability to use the Word of God to moderate his zeal will be quite unproductive. He has been systematically convinced by his "heroes" that he is completely in line with God's Word, which means you will most likely be labeled a doubter or worse—someone who quenches the Holy Spirit.
Here's the thing you have to remember: a lot of what your friend is hearing is absolutely true. That's what makes faith healers so dangerous. The essence of what they say is entirely in line with the truth of God's Word. Their error is much more subtle, and has to do with how they apply those truths.
Your friend has been led to believe that God's power is always activated by our faith, and if we just have enough we will see wonderful and miraculous things take place. The essence of that is true, but faith healers typically ignore two things:
1. God's sovereignty, and
2. God's use of human suffering in His redemptive plan...
...which are two very biblical ideas.
Stumbling Over Sovereignty
People in the hyper-faith movement tend to see God as a one might view a vending machine. They believe if they have the proper amount of faith—much like you would deposit the proper coinage into a machine—you will get what you want. And to be sure, Jesus challenged us to have faith that believes and He made some very wonderful promises concerning that kind of faith. But there are other statements made in God's Word that we have to contend with as well. Such as making sure we ask according to His will. (1 John 5:14)
Faith preachers assume it is always God's will to heal, therefore the only thing standing against a complete healing is a lack of faith or sin. But it is a fundamental error to believe that He always heals whenever we ask by faith. Sometimes God's sovereignty overrules our faith. To believe otherwise reduces God to a genie in a bottle who lives to do our bidding.
God's Redemptive Use for Suffering
Faith preachers rarely allow for the idea that God might have a larger purpose in suffering, despite the fact that Peter wrote, "...he who has suffered in his body is done with sin." 1 Peter 4:1 (NIV)
Do I quote this verse to suggest that God always wants people to suffer and that He will never heal even if we ask? Of course not! God does heal, and it's glorious to see. But there are times when the purpose of our suffering may be veiled to all but God.
The Apostle Paul wrote in 2 Corinthians 12 about a "thorn in my flesh" that God allowed to remain, even after the Apostle asked three times that it be removed. And why? Paul was later made aware that God had a redemptive purpose for that thorn, and as a result he came to the place of actually rejoicing in those things which highlighted his weakness, so that Christ's strength might also be his. (2 Corinthians 12:10)
Honestly, I don't think your friend is going to be won over by a few passages of Scripture. The problem is more systemic in nature. Instead love him, encourage him in the Lord and challenge him in these ideas—specifically with embracing a sovereign God who may choose to overrule the desires of man, and with the Lord's higher redemptive purposes, where even suffering can be used for His glory.
God bless you!