Only a possibility, but because of the similarity of the name, the timeline, location and trade, the below report may relate:
Death of Edward G. Buckenham
Edward G. Buckenham, who was prominent for many years in the trade as a manufacturer of diamond jewelry and as a dealer in diamonds, passed away, Wednesday, at his residence, 54 King St., New York. Mr. Buckenham will be remembered as the head of the firm of Buckenham, Cole & Hall, who were in business for more than a quarter of a century at 10 Maiden Lane.
The deceased was born in London, England, in 1824, and was the son of George Buckenham, a London jeweler. He came to America with his father, in 1839, and the latter soon after became manager of the factory of Ball, Black & Co. Edward G. Buckenham worked with his father for a short time and then for other firms until 1855. When 21 years old he started in business for himself and was afterward joined by George Cole under the style of Buckenham & Cole, who conducted business at the corner of Warren St. and Broadway. The concern later became Buckenham, Cole & Hall and moved to Maiden Lane, where they established a reputation as manufacturers of fine 18 karat diamond jewelry. In 1878 John F. Saunders was admitted and the firm changed to Buckenham, Cole & Saunders, who continued until their dissolution in 1881. Mr. Buckenham then conducted the business alone for a short while and finally retired, 16 years ago. The deceased was a Mason, but was a member of no organization in the trade. He is survived by a wife, two sons and a daughter. The funeral services took place, Friday, from his late residence.
Source: The Jewelers' Circular - 20th March 1901
As stated, the above is perhaps a long shot, but can be removed should further information come to light.
BUCKINGHAM G. (Grimwade p.361)
Moderators: MCB, buckler, silverly
Re: BUCKINGHAM G. (Grimwade p.361)
24 November 1812 George Buckingham Batchelor and Elizabeth Poole Spinster married at Saint Sepulchre Holborn City of London.
2 July 1813 George son of George Buckingham Gold Smith of Bartholomew Close and Elizabeth birth recorded and Saint Bartholomew The Great City of London.
1825-26 George Buckingham recorded paying taxes at Bridgewater Gardens City of London.
(I am not inclined to exclude George Buckenham as a possibility for the subject gentleman at this point.)
2 July 1813 George son of George Buckingham Gold Smith of Bartholomew Close and Elizabeth birth recorded and Saint Bartholomew The Great City of London.
1825-26 George Buckingham recorded paying taxes at Bridgewater Gardens City of London.
(I am not inclined to exclude George Buckenham as a possibility for the subject gentleman at this point.)