Another site lists a Henry Bodine, born 1832, as one of Joseph's children. I wonder if this might be a John Henry Bodine.
From Ronny Bodine:
Obituary, Mount Morris Union Constitution (Mount Morris, N.Y.) of Thurs of 22 June 1865.
DEATH of J. H. BODINE--We regret to announce the death of Mr. John H. Bodine of this village, which occurred on Friday last, after a short illness. Mr. B. was a member of the firm of J. H. Bodine & Co., manufacturers of Agricultural Implements, Machinists, &c. He was a man of untiring industry, of a genial nature, uniformly upright, kind and generous to a fault, and sincerely esteemed as a friend and citizen. Our community share with his relatives in this unexpected bereavement. He was buried on Sunday with Masonic honors a large concourse in attendance.
From New York Federal Census Records:
1860 (15 June) Mount Morris, Livingston Co.: W. H. NOBLE 48 CT dentist, M. A. 42 NY, Elizabeth 22 NY, Emeline BODINE 21 NY.
1870 Mount Morris, Livingstn Co.: Walter NOBEL 59 CT physician, Margaret 53 NY wife, Emma BODINE 31 NY widow, John W. BODINE 6 NY son, Carrie NOBEL 27 NY dau. [Note: The census taker noted relationships in the profession column and they are included here as written.]
1880 (10 June) Mount Morris, Livingston Co.: Walter H. NOBLE 69 CT dentist widowed, Emma M. BODINE 41 NY dau widowed, John W. 15 NY grandson.
From Livingston County Letters of Administration, vol. 3 [1857-1878], p. 158.
On 23 June 1865, Emma N. Bodine and Walter Noble were appointed administrators of the estate of John H. Bodine, of Livingston County, who died intestate.
From Livingston County Wills, vol. 15, p. 331.
The will of Emma N. Bodine, of Mount Morris, written 15 April 1886, was proved 26 July 1886. Therein she devised her entire estate to Carrie F. Nobles, her sister, whom she also appointed her executrix.
Child of John Bodine and Emeline Noble:
John W. Bodine, born about 1865 in Mount Morris, Livingston County, New York; died June 1880-April 1886.
Notes for John W. Bodine:
John Bodine was living June 1880 with his mother, then aged 15, but was not named In the will of his mother, written April 1886.