Pedro de Medina (1548 (1595 ed.), p.119). Curiously, Pedro de Medina says the inscription comes from a "very old" nautical map made by "Tolomeo" at the direction of "Papa Urbano". Presumably, he means a map based on (rather than by) Ptolemy. The last pope by that name was Pope Urban VI (r. 1378-1389). If Medina has not mistaken his popes, and if there was such a map, then that map would contain the oldest reference to Antillia on record.
A rather fancified version of the tale is told in Higginson (1883:p.93), who relates that news of the island's existence was first brought to Europe by an eloping pair of lovers who fled the island.
Cortesão (1954 (1975) pp. 124-5). A similar grant might have been made earlier in 1473 to Infanta D. Brites, of "an island, that appeared beyond the island of Santiago", but was not found when it was sought. ibid.
This objection was already articulated by Vicenzio Formaleoni (1783: p.27-28), one of the first to draw scholarly attention to Antillia.
Babcock (1922: p.148). D'Avezac (1845: p.27) briefly entertained this theory. The Atlantis etymology was also considered, and discarded, by Humboldt (1837: p.192). See Cortesão (1954 (1975): p.118). It has however, remained extant among some modern "Atlantis" theorists. Lewis Spence (1925) suggested that Antilla is the remnant of Atlantis, which had broken up following a natural disaster. Spence (p.87) cites Brasseur de Bourgbourg, Bancroft and Le Plongeon as supporters of this theory, "none of them authorities of any great weight, I fear, and all inclined to rashness."
Alexander von Humboldt (1837) Examen critique, Vol. 2, p.211. This hypothesis was in fact first proposed by Buache (1806: p.27-28). See also d'Avezac (1845: p.27).
According to Barreto (1992: p.163), Ireland had seven cities at the time, which he lists as Cork, Limerick, Waterford, Wexford, Dublin, Dundalk and Belfast, all of which happen to be situated on the coast, at or not too far from bays. However, the author of this article could not find corroboration for Barreto's statement. On a side note, J. Godkin (1867, Ireland and her Churches, p.23) notes that in old Irish churches, a diocese typically had not one, but seven "bishops".
This was first proposed by Hennig (1945) and supported by Armando Cortesão (1954 (1975) p.106). Cortesão (p.74) notes that an inscription about Hercules's "statues" to mark the edge of safe navigation was common practice in Arab charts. Crone (1938) first proposed to read it as Getulliae (Getulia), but later (Crone, 1947) acknowledged the Hercules reading.
List from Armando Cortesão (1954 (1975 ed.): p.156)