Hello. I found a probate notice in the Suffolk County News, Sayville NY dated June 1924. It was about the will of Austin J. Carter, Sr., the executor was Austin J. Carter, Jr. The siblings of Austin, Jr. were Sylvester Carter of Woodhaven and Mrs Marion Varney of Stamford, CT. They filed an objection to the account rendered by the executor, their brother.
1900 US census for Brookhaven, NY shows the family of Austin, Sr but Marion is named "Mary A.". Austin and his parents were born in New York, mother, Anne, was born Ireland, her parents were born England.
Earlier census show us that Austin's parents were Jacob & Hannah Carter still out on Long Island, NY.
I can email the news item and all the pertinent census pages to you if you would like.
Also ... the death date you have for the husband of Mrs. Marion Varney, was actually for the son of Rodney & Marion Varney. The Social Security death index shows us that the Rodney Varney who died in Feb 1988 was born in 1924 and the Stamford Advocate Obituary index shows us his full name was "Rodney Luke Carter Varney".
SSDI VARNEY, RODNEY C., b. 14 Oct 1924, d. 12 Feb 1988, age: 63, last residence on record: 06905 (Stamford, Fairfield, CT), last benefits: 06905 (Stamford, Fairfield, CT), issued: Connecticut, SSN 046-18-5630
Stamford Advocate, date obituary appeared Varney Rodney Luke Carter 2/14/1988 (other ones in the obituary index) Varney Norman A. 9/3/1997 Varney Pierre 6/7/1969 p6 Varney-Regnemer Ethel 1/21/1988 1/22/1988