One of the ablest Calvinistic defenders of continuationism on "Prayer and Ministry in the Power of the Holy Spirit".
Prayer and Ministry in the Power of the Holy Spirit
"...and my speech and my message were not in plausible words of wisdom, but in demonstration of the Spirit and of power, that your faith might not rest in the wisdom of men but in the power of God."- 1 Cor. 2:4-5
"...What works on prayer have been most influential in your life?"
I consider myself a Calvinistic Continuationist similar to Sam Storms, Wayne Grudem, John Piper, Matt Slick, Vincent Cheung, James K. A. Smith et al.
I've arranged the works into 6 groups: Calvinist; Generally Evangelical [usually "Arminian"]; Charismatic and/or Continuationist; Devotional; Biographies; Spiritual Warfare. They are not in any particular order within each division/category. I've excluded books on divine healing and other more specific topics even though they too have shaped my understanding and practice of prayer.
And Yes, I know the problems with the theology of many of the authors I've listed below. For example, Charles Finney sometimes made/wrote Pelagian and Semi-Pelagian statements. But that doesn't mean that God didn't honor the prayers of Finney, "Father Nash" (Daniel Nash) and the host of other Christians involved in the 2nd Great Awakening. Finney was inconsistent. He also sometimes made statement that were anti-Semi-Pelagian. I know that Andrew Wommack and Don Gossett are "Word of Faith" teachers. I know that Vincent Cheung borders on Hyper-Calvinism, is an empirical skeptic due to his modified Clarkian Scripturalism, and is too harsh in his condemnations of cessationists. I know G.H. Lang taught Hyper-Dispensationalism. I know that Derek Prince was part of the disastrous "Shepherding Movement" (of which he recanted), but continued to hold to peculiar teachings like "generational curses" (of which I have no dogmatic stance on). The problems with Neil T. Anderson's anthropology, hamartiology and demonology. ET CETERA, etc......... The list of books I've given are theologically diverse because I believe God's grace is wider than most Reformed and Catholics realize. My theology is eclectic for that reason.
CALVINIST:
A Call To Prayer by J.C. Ryle [HIGHLY RECOMMENDED]
https://www.monergism.com/call-prayer-ebook
Prayer and the Sovereignty of God by Curt Daniel [HIGHLY RECOMMENDED]
http://www.faithbibleonline.net/prayer-and-the-sovereignty-of-god/
God's Sovereignty and Prayer by A.W. Pink [chapter 9 of The Sovereignty of God]
https://www.ccel.org/ccel/pink/sovereignty.xii.html
Prayer and Revelation by Vincent Cheung
https://www.vincentcheung.com/books/Prayer%20and%20Revelation.pdf
More resources by Vincent Cheung on continuationism:
https://charismatamatters.blogspot.com/2013/07/vincent-cheung-on-healing.html
Daily Prayers of Master John Bradford by John Bradfordhttps://www.ccel.org/ccel/bradford/prayers
Of Prayer by John Calvin
https://www.ccel.org/ccel/calvin/prayer
Expositions and Prayers from Calvin
https://ia801407.us.archive.org/31/items/scripturetextswi00calv/scripturetextswi00calv_bw.pdf
With Christ in the School of Prayer by Andrew Murray [HIGHLY RECOMMENDED]
https://www.ccel.org/ccel/murray/prayer
Waiting On God by Andrew Murray [HIGHLY RECOMMENDED]
https://www.ccel.org/ccel/murray/waiting
The Hidden Life of Prayer by David M. M'Intyre [HIGHLY RECOMMENDED]
https://www.monergism.com/hidden-life-prayer-ebook-0
Faith's Checkbook by Charles Spurgeon
https://www.ccel.org/ccel/spurgeon/checkbook
Abide in Christ by Andrew Murray [HIGHLY RECOMMENDED]
http://www.swartzentrover.com/cotor/E-Books/christ/Murray/abide/Abideindex.htm
Spiritual Depression: Its Causes and Cure by D. Martyn Lloyd-Jones
Sermons on which the book was based: https://www.mljtrust.org/free-sermons/spiritual-depression/
GENERALLY EVANGELICAL [usually "Arminian" and/or non-Calvinist]:
The Life of Prayer by A.B. Simpson [HIGHLY RECOMMENDED]
http://www.swartzentrover.com/cotor/E-Books/holiness/Simpson/LifePrayer/TLOP_TOC.htm
How to Pray by R.A. Torrey [HIGHLY RECOMMENDED]
https://www.ccel.org/ccel/torrey/pray
http://www.swartzentrover.com/cotor/E-Books/christ/Torrey/HowPray/HTP_TP.htm
The Complete Works of E.M. Bounds on Prayer [HIGHLY RECOMMENDED]
https://charismatamatters.blogspot.com/2013/08/em-bounds-on-prayer.html
Prevailing Prayer by D.L. Moody
http://www.thecontinuingwitness.com/uploads/9/8/2/3/98238342/prevailing-prayer-what-hinders-it-dwight-l.-moody.pdf
http://www.godrules.net/library/moody/moody.htm
Treatise on Prayer by Edward Henry Bickersteth [Anglican, so might have been a Calvinist]
[HIGHLY RECOMMENDED]
https://archive.org/details/atreatiseonpray00unkngoog/page/n13
https://books.google.com/books/about/A_treatise_on_prayer.html?id=VMAHAAAAQAAJ
Days of Heaven Upon Earth by A.B. Simpson
http://www.swartzentrover.com/cotor/E-Books/holiness/Simpson/Days/Daysindex.htm
The Pursuit of God by A.W. Tozer [HIGHLY RECOMMENDED]
http://www.gutenberg.org/ebooks/25141
Lectures on Revivals of Religion by Charles Finney
http://gospeltruth.net/1868Lect_on_Rev_of_Rel/home68revlec.htm
The Knowledge of the Holy by A.W. Tozer
http://www.heavendwellers.com/hdt_knowledge_of_the_holy.htm
Praying is Working by G.H. Lang (Dispensationalist)
http://www.schoettlepublishing.com/booksonline/lang/praying.htm
Touch the World Through Prayer by Wesley L. Duewel [HIGHLY RECOMMENDED]
Mighty Prevailing Prayer by Wesley L. Duewel [HIGHLY RECOMMENDED]
Daring to Draw Near by John White
Handle With Prayer by Charles Stanley
God's Chosen Fast by Arthur Wallis
Prayer by O. Hallesby
The God Who Hears by W. Bingham Hunter [HIGHLY RECOMMENDED]
My Utmost for His Highest by Oswald Chambers
CHARISMATIC AND/OR CONTINUATIONIST:
A Better Way to Pray by Andrew Wommack
Sermons on the same topic: https://www.awmi.net/audio/audio-teachings/?pid=pw3fQdOQ&lid=ehCTgeWf
There's Dynamite in Praise by Don Gossett
Power in Praise by Merlin R. Carothers
Shaping History Through Prayer and Fasting by Derek Prince
The Secret of Prayer: How and Why We Pray by Enoch Edwin Byrum
https://books.google.com/books?id=hkZGAAAAYAAJ&printsec=frontcover#v=onepage&q&f=false
DEVOTIONAL:
Faith's Checkbook by Charles Spurgeon [Calvinist] [HIGHLY RECOMMENDED]
https://www.ccel.org/ccel/spurgeon/checkbook
Days of Heaven Upon Earth by A.B. Simpson [Evangelical] [HIGHLY RECOMMENDED]
http://www.swartzentrover.com/cotor/E-Books/holiness/Simpson/Days/Daysindex.htm
Morning and Evening by Charles Spurgeon
https://www.ccel.org/ccel/spurgeon/morneve
My Utmost for His Highest by Oswald Chambers [Evangelical]
Expositions and Prayers from Calvin [Calvinist]
https://ia801407.us.archive.org/31/items/scripturetextswi00calv/scripturetextswi00calv_bw.pdf
BIOGRAPHIES:
George Muller: Man of Faith and Miracles by Basil Miller [HIGHLY RECOMMENDED]
The Life of A.W. Tozer: In Pursuit of God by James L. Snyder [HIGHLY RECOMMENDED]
various biographies of John "Praying" Hyde
Remarkable Incidents and Modern Miracles Through Prayer and Faith by G.C. Bevington [autobiography of a Wesleyan]
http://wesley.nnu.edu/wesleyctr/books/0001-0100/HDM0015.pdf
SPIRITUAL WARFARE:
The Bondage Breaker by Neil T. Anderson
The Adversary: The Christian Versus Demon Activity by Mark I. Bubeck
My list of resources on the topic of Divine Healing:
https://charismatamatters.blogspot.com/2013/07/recommended-resources-on-healing.html