The first and foremost problem with the notion of a sinner's prayer is that nowhere does the New Testament assure people of salvation on the basis that they recited a prayer. Scripture nowhere guarantees salvation to people who recite a specific sequence of words. Nowhere do we see the apostles in the Book of Acts assuring people of salvation simply because they recited a prayer. There is neither a prescription nor a description of using sinner's prayer evangelism in Scripture.
Justification in the sight of God is not obtained via formulaic means, but by His grace through faith in the finished work of His Son Jesus Christ. If there exists biblical evidence for reciting a sinner's prayer, then why did the Apostle Paul fail to mention such a concept in his basic presentation of the gospel (1 Corinthians 15:1-4)?
Furthermore, the sinner's prayer has given many unsaved individuals a false assurance of salvation. It has given people a false sense of security in regards to their true standing with the Lord. That is certainly a spiritually dangerous state to be entrapped in. At best, the sinner's prayer contains elements of truth mixed with error.
This is not to communicate the idea that every individual who has recited a sinner's prayer is a false convert, but rather that we should cease implementing that witnessing approach because it is unbiblical and deceptive. It was not until the nineteenth century when a lawyer named Charles Finney invented the sinner's prayer. The concept was drastically popularized by evangelists such as Billy Graham.
It certainly is biblical to guide somebody in prayer or repentance. It is certainly biblical for a sinner to ask God for His forgiveness. The confession of sin is biblical. But assuring a person salvation on the basis of repeating a prayer is wrong. We are saved by the Lord Jesus Christ and His gospel (Romans 1:16-17). We receive Christ by faith (John 1:12-13). It would be wise for us all to examine our doctrine to see whether we are in the faith (2 Corinthians 13:5).