You must mean 1920? to be your gr.gr.?
There are still McInerney's in the telephone book for Clare and at least one in Shragh, Doonbeg
1911: No Michael in Doonbeg but 13 other McInerney's. www.census.nationalarchives.ie
Later birth may not have the Village or Townland Doonbeg.
The Parish is Killard and the Civil Registration Union is
has either another Micheal and Johanna
or this maybe them.
Honor McInerney born 3 June 1880 Michael McInerney & Johanna
Hennessey Querin, Ireland
also same names in Tipperary?
Michael McMcInerny born 02 Apr 1866 #675 Portroe, Tipperary
Michael Inerny and Johanna ........
Mary McInerny born 27 June, 1869 Clare, Michael McInerny
and Johana Hennessy
John McInerny born 22 June 1871, Clare (Johana)
Bridget born Oct 4, 1865, #0359 Kilkee, Clare Johana
You can order copies these birth certificate from the General Registry Office, Dublin www.groireland.ie
note small differences in spellings!