Index Fungorum lists Panaeolina foenisecii (Pers.) Maire as the current name. However, most texts seem to stick with Panaeolus. The ‘Google’ test at the moment (3/21/07) supports Panaeolus over Panaeolina 8 to 1.
First described by Fries as Agaricus foenisecii in 1821. After that it wanders through pretty much all of the dark spored genera. It ends up as Panaeolus by Kuhner in 1926, probably because of the mottled spore development on the lamellae. In 1932 Maire moves it to Paneolina because of the warted ornamentations of the spores. In 1972 Smith puts it into Psathyrella, and has Paneolina as a subsection of the genus Psathyrella. Or so says Smith in his 1972 monograph.

But none of this has the description of Pers., it is all from the type described by Fries. From Index Fungorum, there turns out to be a taxon synonym of Agaricus
foenisecii, from Pers. in 1800, which is before Fries in 1821.

But for now, in the hopes of simplification, Psathyrella, Panaeolus and Paneolina should be considered taxonomic synonyms for this species.