Hi Kieran,
I checked the NY Times for their obituaries. For each (Helen & Henry - aka Harry Bradley), I checked the month they died and the month following their deaths, respectively. I didn't find anything.
The Newspaper Archive website says they have the New York Herald 1764 - 2004. That may or may not be true. If it is like the newspaper archive at Google, there may be large gaps. Newspaper Archive is a paid subscription site but they may offer a trial.
Newspaper Archive
http://newspaperarchive.com/Genealogy Bank didn't come up with your Bradley names, at least when I tried it. They're a paid subscription site too, but I did a freebie search.
http://www.genealogybank.com/gbnk/obituaries/ The NY Public Library - ask them.
Bronx Library Center
http://www.nypl.org/locations/bronx-library-centeror the main branch ...
http://www.nypl.org/ask-nyplThe library has many newspaper holdings on microfilm. They do have the Bronx Press-Review, a weekly paper that has been around since 1940, on microfilm and should have the dates you need <1983:4:14-7:7,21-1985:4:11>
<1985:4:25-1989:12:28>. They also have the New York Daily News archive on microfilm.
And, hopefully, this volunteer is still active:
Obituary Look-up Volunteers, New York
http://freepages.genealogy.rootsweb.ancestry.com/~obitl/volny.htmlLook for "Barbara B." under New York county.
Best of luck Kieran!
Kate