Burnett J. Greene always spelled his last name with an E, as is noted in his dairy from 1880.
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Burnett was a dairy farmer for 50 years on his farm just outside of Franklinville, Cattaraugus County, New York.
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A poem was published in the local newspaper re: his marriage to Sarah Fay:

"The story goes that Cyrus Fay
did lose a daughter the other day;
And yet by all that was plainly seen
the daughter was won to Allen Green.

For he by whom the deed was done,
did prove to be his oldest son,
Yet no great loss, without some gain,
For Cyrus did a son obtain.

And may the union thus formed ________?
Grow brighter, stronger every year,
Until within the realms above
They join in everlasting love."

(Note of explanation by L.G. Greene - Cyrus Fay was the father of Sarah Fay and Allen Green was the father of Burnett Greene)
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OBITUARY FOR BURNETT J. GREENE - 1933
Franklinville: Burnett J. Greene, 72, dropped dead while cranking his car near his home on the Narrows road, west of this village Monday afternoon, July 3rd at 12:30.
Deceased was born in Franklinville, July 14, 1861, and had lived here all his life. His wife, Sarah Fay died 32 years ago. He is survived by one son, Fay Greene of Winfield, Kansas, and one sister, Mrs. Rust of Ellicottville.
Funeral arrangements were delayed pending the arrival of the son from the west.

From M. Graves' Scrapbook of Ischua Valley Historical Society in New York, from local newspaper)
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From Remembrances of Fay Perry Greene Jr., grandson of Burnett: Interviews with his daughter Laura, 1996-1998
I remember my Grandfather Greene very well. He lived on a farm a few miles from Franklinvlile. I belive the farm was on the old road from Franklinville to Ellicottville (Cattaraugus Co. NY). It was quite hilly. He kept cows and horses. One of my early memories is that he put me on a cow's back for a joy ride. Unfortunately for me the cow had other ideas and headed at high speed for the barn. It was a large barn with a divided door. The upper section was closed and I was effectively removed from the cow's back.
Burnett to me was a very jolly outgoing person. He had a good-sized mustache.--hair was a brownish-grey.He had a family that worked for him & that lived on the farm. Their name was Sanford. Mrs Sanford was called "Ev" ! Nigh Olin who married Grace was one of the most personable individuals I've ever met. . I do remember riding in a hay wagon when they were putting up hay--pulled by a team of horses. Ev was blind in one eye from injuries received in an accident--vaguely I think it was the result of being struck by a cow's horn. She didn't wear a glass eye--just had an empty socket there. She did a man's work. Also had a flock of kids. She did it all!!!! --the equivalent of doing it all today & then some!~! I don't remember her husband's first name. It'll probably come to me sooner or later. I would say their family were early settlers. The farm was very hilly. It must have been tough to scratch out a living on it.
I hope we can get back there soon. I think you'll be thrilled with the area. We can find the farm . It's on the Ellicottville---Franklinville road. I doubt if B.J's farmhouse is still standing I found the house my father built on Pine Street--but it was all butchered up by some home-made remodeling.
My father probably sold the farm for a pittance at the height of the depression after B.J.'s death (1933).

Source: 1900 Federal Census Soundex: Ellicottville, Cattauraugus County, NY
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OBITUARY OF SARAH OLIVE FAY GREENE
From The CHRONICLE JOURNAL, dated January 2, 1913 (Front Page) - Franklinville, New York
Mrs. Sarah Olive Greene, wife of Mr. B.J. Greene, died at her residence on Pine Street Dec. 27th, 1912, aged 54 years.
Mrs. Greene had been a patient sufferer of an incurable malady for many years and while her early death was not entirely unexpected, yet it came with a shock to the members of her family as she had been up and about on Christmas Day.
Mrs. Greene was the eldest daughter of our venerable townsman, Mr. Cyrus Fay, and was born and lived always in our town. .She belonged to a family that has been conspicuous in the history of Franklinville for nearly a century, and who for several generations have been men and women of superior intelligence and noted for their high grade of morals both in social and business life. Mrs. Greene was a splendid representative of the family and her generation. To her husband and son she devoted the best energy of her life and as wife and mother she was tender, faithful and true and to the aged members of her family she was devoted to a marked degree, and has been ever willing and eager to minister to their declining years. (-------------------- --------------------unreadable sentence). She was a woman who as long as her health would permit took a lively interest in church and social affairs, and for many years had been a member of the First Presbyterian church. Mrs. Greene possessed a bright mind, sparkling with intelligence and was always interesting in conversation. She was a kindly and generous neighbor and a faithful friend, and true in all things to the memory of her distinguished ancestors. She died just as she had entered a new and beautiful home, just at the summit of Life's steep hill, where the decline on the other side looked so inviting and pleasant, with here and there a shady spot to sit down and rest and drink from the cool spring of memory and see the golden glory of the setting sun. She had a Christian's hope and a Christians courage and realizing that her end was near, bade her family good-bye and sank into peaceful sleep to awake at the dawn of eternal day.
The funeral was held from the family residence on Pine street the 29th inst., Rev. Higibotham officiating, and was largely attended.
Those of the immediate family who mourn her loss is her husband, Mr. B.J. Greene, an only son, Fay P. Greene and her venerable father, Cyrus Fay. Also one sister, Mrs. E. E. Litchfield.
Those from out of town attending were: Mr. and Mrs. E.E. Litchfield, Ellicottville; John Fay, Dundee, Io; Dr. James J. Cole, Oelwein, Ia.;Mrs. Frank Hopkins, Salamanca; Mrs.and Mrs. E.E. Rust and Mr. and Mrs. N.T. Olin, Ellicottville; Mrs. George Williams, Machias; Mrs. Harriett Baker, LeMar, Ia.; Mrs. Dr. (sic) Baker, Clyde Ohio; Mr. A.B. Clark and Miss Isabel Clark, Buffalo; Mr. John Pierce and Mr. and Mrs. William Pierce, Machias.
By request, M.H.W.
(Below obituary:)
CARD OF THANKS
We wish in this manner to express our thanks to the neighbors and friends who kindly assisted us in our time of bereavement. Especially would we remember those who furnished flowers, and the choir.
B.J. Greene and family