I love topics like this; no matter how complete I think my library is, without fail I find something new to me. In this case it was Lavery's book on arming and fitting ships of war.
As for the original question; so far as I know, there is no complete and authoritative technical guide to naval armament in the black power era, so you will have to find mostly bits and pieces here and there. There just might be a university dissertation on the topic, but here again I am not aware of one-if you have access to university databases for theses and dissertations you might find something useful-I have a few technical articles on gunpowder development throughout the world I've found that way. Anyway, we might be able to provide more focused guidance if you could tell us what you want to know about black powder naval guns. Are you most interested, for example, in cannon development, manufacturing, or in what armament was carried by which ships?
The latter, for example, can probably best be answered by books about specific naval engagements. Skaggs and Altoff's "A Signal Victory, The Lake Erie Campaign 1812-1813," for example, has an appendix listing the British armament at the battle. And the armament carried by the various ships of the Napoleonic wars can mostly be found in various books about the navies, navall wars or the battles in those wars. So, for example, Lavery's "Nelson's Navy," and Blake and Lawrence's "The Illustrated Companion to Nelson's Navy" have useful information about the guns carried by various classes of ships
BTW, before I forget, a google books pdf copy of the 1815 edition of "Falconer's Dictionary of the Marine," but the original and not the 2006-reprint, can be found at:
link
Pdf or kindle copies of the original 18th century publication of Falconer's can be found on the internet archive and at Gutenberg.
As for 18th century navies, Jack Coggins' "Ships and Seamen of the American Revolution" has some interesting details and drawings of AWI naval guns (Coggins was a graphic artist and friend of Fletcher Pratt who played in Pratt's 1940s naval war games, so there's a wargaming connection there).
As for earlier periods, John Guilmartin's "Gunpowder and Galleys" has lots of information about Renaissance naval warfare, including info about the guns. Bert Hall's "Weapons and Warfare in Renaissance Europe" is mostly concerned with land warfare, but it has detailed information about technological development including gunpowder manufacturing.
John Norris's "Gunpowder Artillery 1600-1700" is mostly concerned with land warfare, but it has a few bits on naval artillery of the period.
BTW, it would probably be worth your while to thumb through the bibliography of any book you find on period naval warfare as that is probably the best way to get a lead on older books on the topic.
As for more distantly related possibilities, Carlo Cipolla's "Guns, Sails and Empires, Technological Innovations and the Early Phases of European Expansion" is pretty much as described by the title.
A very interesting, but hard-to-find, article about 18th Century Spanish Navy acquisition of cannon is Agustin Gonzalez Enciso's "Buying cannons outside: when, why, how many? The supplying of foreign iron cannons for the Spanish Navy in the eighteenth century," a symposium paper reprinted in "The Contractor State and Its Implications, 1659-1815." Most of the rest of the book has pretty much nothing to do with the op's topic, but the articles are interesting if generally somewhat unusual as should be expected from the products of modern scholarship and a symposium on the state as contractor for military goods and services.
So there's a start; if you can give us a more detailed idea of what you are looking for perhaps we can add to the list.
paints his first three ships from the starter set.
