Randy Gibbons provides a good overview of the books and methods available for self-teaching. Among the books now online are the 1887 edition of the Orbis Pictus of Comenius and Kendrick’s 1851 Greek Ollendorff.
W.H.D. Rouse was a pioneer of the Direct Method at the Perse School in England. Recordings here with a commendable effort at rendering the pitch accent. Rouse’s Greek Boy at Home, also available in a Focus reprint, seems to be catching on among speakers of Spanish here and here.
John Stuart Blackie seems to have spearheaded a revival of spoken Greek in Scotland: his Primer (1891) and Dialogues (1871) are glimpses into a vanished and contrafactual world where topics from ice-skating to Highland dress are open to discussion.
Mogyoróssy Arkád, alias Arcadius Avellanus, is rumored to have learned Latin before his native Hungarian. His textbook Palaestra was published serially from Williamstown, Brooklyn, and New York City between 1912 and 1919. He also translated Treasure Island into Latin as Insula Thesauraria. He has very strongly held and hostile opinions about German scholarship, but Palaestra has the feel of being written by a native speaker, with many insights into colloquial and practical use.