Ilocated what may be the burial/death index for your James Barrett at the Irish Family History Foundation (IFHF) website for County Donegal. The index shows he was buried from the Iniskeel Church of Ireland (CI) in 1893:
1 match for the search criteria: Barrett (plus variants) James 1893 Parish: INNISKEEL (CI)
Record Type: Burial/Death Records for Co. Donegal Surname: Barrett First Name: James
Before you begin searching for ancestors at the IFHF website you first need to establish an account. Indexes are free to search, but to download a birth, baptism, marriage, or death transcription costs 5.00 Euros payable by credit card. Once the credit card payment is received a transcription of the record you are interested in, will be sent to your computer.
I’m not sure what information will be found in the record for James Barrett. The name of the place of burial may not be indicated.
I also located the burial/death indexes for several more Barretts buried from the Iniskeel Church of Ireland at the IFHF website. These follow:
Church BurialBarrett Olicia 1834 Co. Donegal
Church Burial Barrett Eleanor 1844 Co. Donegal
Church Burial Barrett Ellen 1848 Co. Donegal
Church Burial Barrett Archibald 1857 Co. Donegal
Church Burial Barrett James 1859 Co. Donegal
Church Burial Barrett James 1861 Co. Donegal ____
You may be able to get more information about the the Iniskeel burials and graveyards from the local priest in charge of the parish, John Deane.
Contact information follows:
Rev. J Deane - Bishop's curate The Rectory, Ardara Co Donegal