I think he is also known as Jonas D. Foskett. If you Google that name, you will find he was born May 23, 1830 in Boston per the Foskett family genealogist.

Youngest son of Ezra Foskett (1787, MA - Feb. 11, 1863, Boston) and Mahala Osborn Foskett (1789, MA - Feb. 12, 1861, NYC) - with whom he is enumerated in NYC 1850 census.

James Foskett,age 30, born MA, hotel keeper, personal estate $350, is enumerated with Ezra and Mahalah Foskett in the 1860 New York City census ( Foskett name is mangled by Ancestry.com as Fsdett).

James D. Foskett (without occupation) is enumerated in the Boston 1870 census living with Lydia, the widow of his brother, Ebenezer Foskett. Ebenezer Foskett was a piano-forte maker (work for Chickering pianos Boston?) who dies in Roxbury,MA, April 19, 1867. The father, Ezra Foskett, is mentioned as dying "at Chickering, Tremont St., Boston" which was site of piano factory). Ebenezer Foskett's sons were also in music business.

Jonas D. Foskett dies in Boston September 23, 1870 - he is not married. Mass. State Archives vital records index online lists Jonas D. Foskett death as Boston 1870, vol. 231, p. 163.

Death records can be ordered easily by mail. Boston wills and administrations could be checked. Newspaper obituaries? A project for someone in Boston.

If you examine the family death dates, it explains living arrangements and moves from New York City to Boston. I could be wrong - but this seems right and possibly explains why Foskett has been so hard to find.