Where I attend, we have a period of time during Sunday Morning Worship called The Garden of Prayer. It normally occurs just prior to communion and is accomplished by Church Elders along with their wives moving from their pew seats to different locations in the aisles to be available for prayer requests. Members/attendees so desiring prayers go to the Elder & wife of their choice and make the request and the Elder leads a prayer for the reason requested. Something that has me puzzled is that a newly appointed Elder has begun having his wife lead the prayer in that small group setting within the Worship Assembly. Since this is Worship Assembly, this seems inappropriate since a private prayer does not seem possible in a public setting. Also, if the requestor of the prayer is asking the prayer be lead by the Elder's wife, it would seem necessary for the wife and requestor to move to a private area outside the Worship Assembly to accomplish their task. However, on one occasion, I observed the Elder ask his wife if she wanted to lead the prayer - clearly the request for the Elder's wife to lead the prayer was the Elder and not the requestor. Your comments within this website indicate one cannot pass their own authority on to another if it is prohibited by scripture. Although God does gives us minor room to decide in some areas, I do not believe that would be allowed in this instance.
While this question is not addressed to the practice denominated "The Garden of Prayer," it should perhaps be the first thing addressed. Elders in the body of Christ should be wise enough and sufficiently grounded in scripture to know that people are not changed, except emotionally, by programs that seek new ways to engage in even scriptural activities. Such practices from swaying with lifted hands to applause, to having people wander around the assembly to pray in small groups cannot change people in any way but emotionally. They are temporary external practices seeking to make permanent internal changes. That is not God's method. He seeks to permanently change people externally by making permanent internal changes.
The described practice, assuming a scriptural justification for the practice was sought, is probably founded upon James 5:14 (see the discussion of this verse on this website in the Lessons on James). The context of the assembly is not the worship assembly. It is a sickroom from which the one ill or those caring for him call for the elders (not an elder) to come to his bedside, pray for him, and anoint him with oil. In the passage the elders go to the sick, not the sick to the elders in the worship assembly. The elders all pray ("let them"), not just one. The elders' wives are not mentioned among the called. Clearly the verse does not justify the practice described.
But does that mean that the practice is unscriptural? Not necessarily. Are there other principles that are applicable? First, consider the nature of the public worship. It is called so that the whole church can come together into one place and simultaneously participate in the public acts of worship (for example, "eat the Lord's supper," 1 Cor. 11:20). It is to be conducted in a manner that is decent and in order 1 Cor. 14:40), not characterized by all praying or speaking at the same time. God is not a God of confusion, but of peace, as in all churches of the saints (1 Cor. 14:33). One good test is to determine whether the same principle could be applied in other acts of worship. Would it be appropriate to have different groups simultaneously singing different songs? Preaching and hearing different sermons because their needs are different? Clearly not. This alone should answer the question.
There is one other issue, however – at least one wife of an elder has been asked to lead prayer. There is no reasonable argument that this practice can be called private prayer because it is part of the public assembly. Nor is it possible to claim that it is family prayer. It is certainly a spiritual family, but if that justifies a woman's leading prayer, should it not also justify a woman's preaching or leading worship in some other capacity? This issue is addressed in a number of the "Questions and Answers" and in "Bible Classes:Questions, Lesson 4." The described practice violates these principles and is, therefore, wrong.
One last comment – even if it were lawful, it is not expedient (1 Cor.6:12; 10:23)
You Must Hear the Gospel
You must hear the gospel and then understand and recognize that you are lost without Jesus Christ no matter who you are and no matter what your background is. The Bible tells us that “all have sinned, and come short of the glory of God.” (Romans 3:23) Before you can be saved, you must understand that you are lost and that the only way to be saved is by obedience to the gospel of Jesus Christ. (2 Thessalonians 1:8) Jesus said, “I am the way, the truth, and the life: no man cometh unto the Father, but by me.” (John 14:6) “Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.” (Acts 4:12) "So then faith cometh by hearing, and hearing by the word of God." (Romans 10:17)
You Must Believe
You must believe and have faith in God because “without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.” (Hebrews 11:6) But neither belief alone nor faith alone is sufficient to save. (James 2:19; James 2:24; Matthew 7:21)
You Must Repent
You must repent of your sins. (Acts 3:19) But repentance alone is not enough. The so-called “Sinner’s Prayer” that you hear so much about today from denominational preachers does not appear anywhere in the Bible. Indeed, nowhere in the Bible was anyone ever told to pray the “Sinner’s Prayer” to be saved. By contrast, there are numerous examples showing that prayer alone does not save. Saul, for example, prayed following his meeting with Jesus on the road to Damascus (Acts 9:11), but Saul was still in his sins when Ananias met him three days later (Acts 22:16). Cornelius prayed to God always, and yet there was something else he needed to do to be saved (Acts 10:2, 6, 33, 48). If prayer alone did not save Saul or Cornelius, prayer alone will not save you. You must obey the gospel. (2 Thess. 1:8)
You Must Confess
You must confess that Jesus Christ is the Son of God. (Romans 10:9-10) Note that you do NOT need to make Jesus “Lord of your life.” Why? Because Jesus is already Lord of your life whether or not you have obeyed his gospel. Indeed, we obey him, not to make him Lord, but because he already is Lord. (Acts 2:36) Also, no one in the Bible was ever told to just “accept Jesus as your personal savior.” We must confess that Jesus is the Son of God, but, as with faith and repentance, confession alone does not save. (Matthew 7:21)
You Must Be Baptized
Having believed, repented, and confessed that Jesus is the Son of God, you must be baptized for the remission of your sins. (Acts 2:38) It is at this point (and not before) that your sins are forgiven. (Acts 22:16) It is impossible to proclaim the gospel of Jesus Christ without teaching the absolute necessity of baptism for salvation. (Acts 8:35-36; Romans 6:3-4; 1 Peter 3:21) Anyone who responds to the question in Acts 2:37 with an answer that contradicts Acts 2:38 is NOT proclaiming the gospel of Jesus Christ!
You Must Be Faithful Unto Death
Once you are saved, God adds you to his church and writes your name in the Book of Life. (Acts 2:47; Philippians 4:3) To continue in God’s grace, you must continue to serve God faithfully until death. Unless they remain faithful, those who are in God’s grace will fall from grace, and those whose names are in the Book of Life will have their names blotted out of that book. (Revelation 2:10; Revelation 3:5; Galatians 5:4)