I was very pleasantly surprised when less than a week later I received a naturalization document with information I had been hoping to find for many years.
Below is some of what the document says.
John Ducy of West Brookfield, in the
C[ounty] of Worcester, an alien and a free white person, rep[resents] that he was born at Sillow in County of Waterford, Ireland, on or a[bout] Month of December, in the year one thousand eight [hundred] and fifteen, and is now about thirty-six years of age: that he ar[rived ?] New York in the State of New York on the Month of April, in the year one thousand eight hundred thirty nine; that it is his bona fide intention to become a Citizen of the United [States of ] America, and to renounce forever all allegiance and fidelity to any foreign Prince, Potentate, State, and Sovereignt[y ?] ever and particularly to Victoria Queen of Great Britain and Ireland, whose subject he has heretofor[e?] All which together with his declaration thereof on oath, before the Albany Justice Court in t[he] County of Albany appears in the records of said court, to wit: on the first day of December
And said petitioner further represents, that he has ever since continued to reside within the jurisdiction [ ] United States, to wit: West Brookfield, New Braintree, North Brookfield, Charl[ton] and Worcester in the County of Worcester.
The document goes on to name witnesses Donald Donah[ue] and Cornelius Donahue of Worcester, in the County of Worcester who say that they have known the petitioner for five years during which time he has been a resident of West Brookfield in the said county.
Whereupon the Court here, to wit: on the first day of October  during said term, admit the said John Ducy to become a Citi[zen of the] United States of America; and order that the record thereof be made accordingly.
Attest: Wm. L. Smith Asst. Clerk
This was a great find! I now have more specific date and place of birth, and a year of immigration. I know that John Ducy immigrated earlier than the famine immigrants, and after consulting an expert, I know that he possibly worked on the railroad which ran between Worcester, MA and Albany, New York.
I have not yet found Sillow in County Waterford, and do not know if Sillow is a religious or civil name, or even if it is spelled correctly. I am hoping to spend more time looking into the information in the document.