Our sole source for this article is Smith's Origins of Biblical Monotheism .
Adonis is reckoned an ancient deity, but the only account of his death comes from a text dated to the second century -- too late to influence the story of Jesus -- in which it is described how his death at the hands of a boar was mourned by worshippers in Byblos. After mourning, worshippers the next day "proclaim that he lives and send him into the air."
Is this a "resurrection"? It sounds much more like Roman apotheosis (exaltation via the ascent of the spirit) as stated; in any event no method of getting alive again is described. Other rituals known for Adonis seem to connect him to vegetation, and accentuate his death, with "no hint of rebirth." J. Z. Smith, the scholar of the history of religions, notes that "classical accounts of Adonis neither mention nor describe his rising from death and that only accounts fashioned by Christian writers introduces the theme of Adonis's resurrection." This is too little, too late to influence the story of Jesus.
Other characteristics of Adonis are no help for copycat theorists: He is young and good-looking, a lousy hunter, and "a paragon of anti-heroic behavior." Nothing bears a likeness to Jesus here. One specific offered by copycat theorists Freke and Gandy is that Adonis had a "virgin mother" named Myrrha and a comparison is made between communion and "the bones of the dead Adonis" which were "said to be ground on a mill and then scattered to the wind."
The latter claim is derived from Frazer and is such an enormous non-parallel that it deserves no comment, unless one wishes to add that Adonisian communion consisted of running around in the wind catching Adonis' ashes in cups and between slices of bread. The former I find verified nowhere.
Finally it is said that "Icthys" (as in the Christian fish symbol) "had for centuries been the Greek name for Adonis", a matter which, if true, we consider conceptually refuted by the linked article.
In short, this is yet another unprofitable proposition for the copycat theorist.