Here are a few suggestions to start with. I might add more if I get ambitious. I've been going through a Google Books search of 19th century works on prayer and choosing only those that are substantial treatises by important authors and that are available as free e-books online.
Others feel free to add to this list. Only books that would be considered "classics" due to how well known their author was or their influence on other important authors, and only ones that are out of copyright (older than 75 years, generally). And if you're going to add suggestions, please do the research to find publication info and where Faithlife can find a digital copy online, and a brief bio of the author justifying his or her inclusion).
- Prayer, the Key of Salvation by Michael Müller (Baltimore: Kelly and Piet, 1868) - free on Google Books; full text available here (Fr. Michael Müller C.Ss.R. (1825–1899) was a prolific Catholic writer of the 19th century in the United States.)
- The Spirit of Prayer by Hannah More (London: T. Cadell, Strand, 1825) - free on Google Books (Hannah More is listed in The Top 100 Women of the Christian Faith; need I say more?)
- Reflections on Prayer and on the errors which may prevent its efficacy by Hannah More (Philadelphia: Anthony Finley, 1820) - free on Google Books
- A Short Treatise on Prayer by St. Alphonsus Liguori (Dublin: John Coyne, 1834) - free on Google Books (Alphonsus Maria de' Liguori, C.Ss.R. [27 September 1696 – 1 August 1787], was an Italian Catholic bishop, spiritual writer, composer, scholastic philosopher, and theologian. He founded the Congregation of the Most Holy Redeemer [the Redemptorists].)
- Thoughts on Public Prayer by Samuel Miller (Philadelphia: Presbyterian Board of Publication, 1849) - free on Google Books (Samuel Miller was Professor of Ecclesiastical History and Church Government at Princeton Theological Seminary, and was also integral in founding the institution. He is perhaps best known for the theological, polemical, and biographical writings he published throughout his life.)
- The Gift of Prayer by Thomas Mann (London: Thomas Ward and Co., 1840) - free on Google Books (Thomas Mann was not the more famous man by the same name; he was minister of Sun Hill Chapel, West Cowes, England; but this book is in the Bodleian Library and looks like a gem, just from browsing the Table of Contents).
- A Treatise on Prayer: Designed to Assist in Its Devout Discharge by Edward Bickersteth (Schenectady: A. Van Santvoord & M. Cole, 1822) - free on Google Books (Edward Bickersteth was Bishop of Exeter)
- A Method for Prayer by Matthew Henry (Edinburgh: Ogle & Aikman, 1803) - free on Google Books (Matthew Henry was the Matthew Henry who wrote the famous commentary)
- The Privie Key of Heaven; or Twenty Arguments for Closet-Prayer by Thomas Brooks (Llanfyllin: Richard Pugh, 1820; first published in 1665) - free on Google Books (Thomas Brooks [1608–1680] was an English non-conformist Puritan preacher and author. He was one of the casualties of the Great Ejection following the Act of Uniformity 1662 in England.)
- The Bible History of Prayer by Charles Augustus Goodrich (Hartford: Case, Tiffany & Co., 1851; originally published earlier, ca. 1847) - free on Google Books (Charles Augustus Goodrich [1790–June 4, 1862] was an American author and Congregational minister, who popularized the motto "a place for everything and everything in its place." He was also a member of the Connecticut Senate.)
