Such an assertion begs debate. Debate that would begin with a clearer definition of the idea of "prodigy," which combines ideas of omens, miraculousness, precocious genius, and technical mastery. Some disciplines seem fertile for prodigies: math, chess, physics, and music. In the first three, judging the prodigy as prodigious seems easier: the prodigy solves a problem or wins the game. In the fourth, the prodigy's prodigiousness is more difficult to gauge: the prodigy can play with mastery, but I would have to defer to people more knowledgeable in music to be able to differentiate between a human-playback machine and a true genius.
In literature, the field I know much better, we decided that the prodigy's work as a youth would have to be of such quality that it demanded comparision to the productions of serious writers of all ages. This definition would rule out Byron's Hours of Idleness (produced at 18), or Pope's later assertion that he "lisped in rhyme": no matter how much potential was shown, the output doesn't deserve to be taken seriously.
Keats, despite his sudden brilliance and youth, was 23 or 24 during the "golden year." Chatterton's poetry, written before his 20th birthday, is largely forgotten today--the deception that was his downfall also covers up his voice. Gerard de Nerval was heralded as a prodigy, for translating with great sensitivity Goethe's Faust--does that count? (And in another, perhaps related discipline, Hume has got to be one of the few philosophy prodigies; his Treatise was conceived before 21 and written before 25. Maybe that's beyond the cut-off date.)
I don't think it's an accident that when looking for literary prodigies, I'm first looking for poets. The lyric would seem to be the easiest mode to write in without wide and deep experience of life. You'll see a lyrical novel here and there--Alfred de Musset's Confessions d'un enfant du siecle at age 26 might qualify him as a prodigy, as might his poetry collection at twenty, Contes d'Espagne et d'Italie.
So many of my examples are drawn from the early 19th century, an era that glorified youth (and that presented fewer obstacles to publication), so where are the later literary prodigies, or contestants thereunto?