Where Can I Find The Sinner's Prayer?

I need some help, please. I have been preaching and teaching the bible for most of my adult life, yet I am having trouble finding the “sinner’s prayer” in the bible. I know it must be there some place, as most of the denominations say that is the path to forgiveness and salvation.
I have found where Paul said, “So faith comes from hearing, and hearing by the word of Christ [God, KJV]” (Romans 10:17). I also have found where Peter said, “Repent, and each of you be baptized in the name of Jesus Christ for the forgiveness of your sins; and you will receive the gift of the Holy Spirit” (Acts 2:38). But I have not found the “sinner’s prayer.” I have looked and still it eludes me along with the accompaning, “Let Jesus come into your heart.” Am I missing something?
I look in the bible and I find where Jesus told those around Him, “Therefore everyone who confesses Me before men, I will also confess him before My Father who is in heaven” (Matthew 10:32) and the Apostle Paul said, “with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation” (Romans 10:10). But I still haven’t found the “sinner’s prayer.”
Once again, I look into my bible and find, “Be faithful until death, and I will give you the crown of life” Revelation 2:10). But I haven’t found, “Let Jesus come into you heart and/or the “sinner’s prayer.” Am I just not looking in the right place? Is my bible not complete? If the way to heaven is through, “Let Jesus come into your heart and say the sinner’s prayer,” shouldn’t I be able to find it said in the bible?
Friends, I do not mean to sound harsh or unkind, but if we cannot find it in the bible, it must not be true (John 17:17). Please, I urge you, repent and be baptized so that your sins might be forgiven by God. That is the only way I find in the bible to salvation (1 Peter 3:21).