Green’s Dictionary of Slang

(Irish) to reduce, to ‘take down a peg’; also as vtr. to diminish one’s activity.

1910		Wigan Obs. 15 Jan. 12/4: They said they would have a bit of fun out of the ‘old woman’ [...] The ‘old man‘ said it would ‘soften her cough’ a bit.
1910		Dublin Eve. Teleg. 28 June 3/7: ‘Graham came towards me in fighting attitude [...] so I gave him a few ‘clatters’ to ‘soften his cough’.
1993		Irish Indep. 8 Sept. 15/4: A couple of thundering displays at centre-back [...] would certainly soften the cough of the critics.
1997		Irish Times 11 Jan. 🌐 ireThere is a number you dial and, lo and behold, don’t you get the number of the friend who has just hung up. That will soften the cough of those people who can’t be bothered to leave a few short and courteous words on the answering machine .
2002		Irish Indep. 4 Nov. 14/3: Will the Revenue soften its cough next year in the face of litigation and political pressure.