Learn English – origin of phrase ‘stone the crows’

Etymonline offers no insight. The British National Corpus has three cites from 1989, 1991, and 1992. The Corpus of Historical American English has two cites, from 1981 and 1986. Wiktionary doesn't say anything about etymology, but marks the phrase as UK, Australian, and has a much older cite from Rose Of Spadgers by C. J. Dennis, 1924. The most extensive discussion I have found so far is over at The Phrase Finder:

There have been a few attempts to explain the origin of this odd phrase. [...] The more prosaic suggestion — that it alludes to the practise of throwing stones at crows — is much more likely.

I've found mid-20th century references from England that describe it as an Americanism and American newspaper articles that call it 'an old English phrase'. The dates of those are more or less right but not the locations — the phrase appears to have originated in Australia. Most of the early citations in print come from down under. It has a sort of Australian twang to it and is in common with several other similar phrases, all with the same meaning: starve the bardies [bardies are grubs], stiffen the crows, spare the crow.

Partridge also lists "starve the bardies or lizards or mopokes or wombats", marking them all as Australian expletives, and noting that "Wombats may also be speeded".