Thanks to the wise people of Mudcat.org, I discovered that had arranged some Irish songs.
One of the songs Beethoven arranged was called O would I were but that sweet linnet, the words of which had been written by William Smyth. Thomas Moore noted in his journal that Smyth had rewritten many of his Irish Melodies and sold them as new compositions, O would I were but that sweet linnet being lifted from The valley lay smiling before me (O’Rourke, Prince of Breffni). This song, a lament for Tigernán Ua Ruairc, is set to the tune of Cailín Deas Crúite na mBó. Smyth’s effort was little more than doggerel, but his appropriation was plausible enough to fool one of the greatest composers of all time into believing that it was culturally authentic.
Some more background is below:
George Thomson (1757-1851) of Glasgow, Scotland, was a publisher and collector of folk songs. He commissioned composers of his day to set the folksongs, paying them well. Among the composers who took Thomson up on his offer were the Austrian Ignaz Josef Pleyel, the Bohemian Leopold Kozeluch, Franz Joseph Haydn, and even Ludwig van Beethoven.
Beethoven began his folksong settings in 1809 and continued with them off and on until 1820. Beethoven spent considerable time on the folksong settings and attempted to make them of real musical interest. Most of the folksong settings are for voice with a piano trio accompaniment (piano, violin and cello), and are not simple settings. While Thomson was most interested in British Isles songs, Beethoven expanded his own scope to include German, Danish, Tyrolean, Polish, Spanish, Russian, Hungarian and Italian texts, even though Thomson would only publish the Scottish, Irish, Welsh and other British songs.All in all, Beethoven wrote approximately 64 Irish songs, most of which were published in the groups Twenty-five Irish Songs (WoO 152, 1814), Twenty Irish Songs (WoO 153, 1814-1816), and Twelve Irish Songs (WoO 154, 1816), all published in Edinburgh and London. Source.