I have some pre federation rolls for NSW, hardcopy so not easy to search through.
Coonamble was its own Police District, and was within the electorate of The Bogan. I have not found HOWER on my paper copies, sorry.
You mention that you have BDM certs .... do these indicate if they refer to the town or could they be referring to the Police District, or perhaps to the NSW BDM district (all slightly different geographical areas, meant to test the FH buffs searching for Neil's dead rats !).
May I ask why you are seeking the info, perhaps there's an alterative way to find it for you.... eg 1903 NSW ER .... this is when females became eligible to enrol in NSW. Of course it was not yet compulsory.
Cheers, JM