Keyboard Sonatinas Nos. 5, 10 and Flute Sonata No. 4, by Ignace Pleyel, c. 1785-95.
"... and Mary, at the end of a long concerto, was glad to purchase praise and gratitude by Scotch and Irish airs,..." (Pride and Prejudice Volume I, Chapter 6, p.17-18)
The distinction between popular and art music was far more fluid in Austen's time than it would become in the latter half of the nineteenth century -- both Mary's long concerto and her crowd-pleasing songs could well have been by the same composer. Above, a link to an album of vocal and instrumental works by Ignace Pleyel that were in Austen's own library.
Mary's Scottish songs are quite possibly from one of the various collections of Original Scottish Airs edited by George Thomson. The lyrics in these volumes are mostly adaptations of traditional Scottish songs by renowned Scottish poets (Joanna Baillie, Robert Burns, and Walter Scott all worked for Thomson at various times). The song melodies are also generally traditional, but arranged for modern instruments and modern musical taste. Pleyel was Thomson's sole arranger in the early years; he would be replaced by a succession of composers, among them Haydn and Beethoven.
The collections, which were published between 1793 and 1841, were a minor success both in England and on the Continent, appealing to a widespread taste for "folk" material. One imagines Mary might have purchased praise with one of the more comic songs: "Hooly and Fairly," for instance, in which a husband laments his wife's heavy drinking.
Source: Naxos Music Library.