Which body's discovery in 1930 came from a systematic search for a planet that was not there?

Pluto. Percival Lowell had predicted a Planet X from apparent irregularities in the orbits of Uranus and Neptune, and his observatory kept hunting after his death. Clyde Tombaugh, a Kansas farm boy hired on the strength of drawings he had sent in, found it in 1930 by blinking pairs of photographic plates taken days apart, looking for the one dot that moved.

The irregularities were not real. They came from a slightly wrong mass for Neptune, corrected by Voyager 2 in 1989, and Pluto is far too small to have caused them anyway - it is smaller than our Moon. So the prediction was wrong, the search based on it was thorough, and the thing it found was a genuine discovery that had nothing to do with the reason for looking.

It was demoted in 2006 when the same region kept producing comparable objects - Eris, initially thought larger, forced the question of whether the solar system had nine planets or dozens. The definition adopted requires a planet to have cleared its orbital neighbourhood, which Pluto has not; the vote was taken at the end of a conference by a fraction of the members, and astronomers have been arguing about it ever since. The name was suggested by an eleven-year-old in Oxford.