When did prodigies stop being evil?

The OED lists five senses of the noun prodigy from Latin prodigium. The date range for the examples given for each of them are shown.

1. An extraordinary thing or occurrence regarded as an omen; a sign, a portent. Now rare. Circa 1450 - 1991

2. An unusual or extraordinary thing or occurrence; an anomaly; something abnormal or unnatural; spec. a monster, a freak. 1595 - 2004.

3a. An amazing or surprising thing; a wonder, a marvel. 1616 - 1988

3b. A wonderful or outstanding example of a specified attribute, achievement, etc. 1647 - 1993

3c. A person with exceptional qualities or abilities esp. a precociously talented child. Frequently with appositive modifying word, as child prodigy, infant prodigy, etc. 1684 - 1991

Hence, all of them have relatively current entries. However, sense 1 seems to reflect the meaning you describe of a prodigy being "demonic", and in that case there is no entry between 1882 and 1991, and the latter does seem to refer back to a classical matter. Those two examples are given below, and I would therefore deduce that the the omen,sign,portent meaning ceased around the end of the nineteenth century.

1882 F. W. Farrar Early Days Christianity I. 73 The air was full of prodigies. There were terrible storms; the plague wrought fearful ravages.

1991 Classical Q. New Ser. 41 318 The prodigy of Hippokrates' pots overboiling firelessly at Olympia earns immediate disapprobative notice.

The term has different connotations, one is "something abnormal or monstrous" even though it is not the more common:

Prodigy

• late 15c., "sign, portent, something extraordinary from which omens are drawn," from Latin prodigium "prophetic sign, omen, portent, prodigy," from pro "forth, before" (see pro-) + -igium, a suffix or word of unknown origin, perhaps from the same source as aio "I say" (see adage). Meaning "child with exceptional abilities" first recorded 1650s.

Prodigy

(now rare) An extraordinary thing seen as an omen; a portent. [from 15th c.]

• 1971, Keith Thomas, Religion and the Decline of Magic, Folio Society 2012, p. 87: John Foxe believed that special prodigies had heralded the Reformation. An extraordinary occurrence or creature; an anomaly, especially a monster;

a freak. [from 16th c.]

An amazing or marvellous thing; a wonder. [from 17th c.]

A wonderful example of something. [from 17th c.]

An extremely talented person, especially a child. [from 17th c.]

(Wiktionary)