George,
You can view John Chambers death certificate on-line on the GRONI site. He died 14.10.1876 and the place of registration is Lisnaskea. You may find that his relationship to Thomas & Martha will be confirmed by the informant. You can view the original certificate on-line on the GRONI website, using the “search registrations” option:
https://geni.nidirect.gov.uk
You will need to open an account and buy some credits. It costs £2.50 (sterling) to a view a certificate.
The informant for Thomas & Martha’s deaths was Edward Nelson. This looks to be him in the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Rosslea/Tatt…
Edward Nelson acquired the Chambers farm in 1899 (according to the Valuation revision records) but was replaced by Thomas Hazzelet in 1901. So evidently Martha left her farm to Edward. Perhaps he was a distant relation?
Looking at the Chambers households in Fermanagh in the 1901 census, the majority were Church of Ireland so I’d expect that your family were too. The main parish church is in Clones and has records as follows:
Baptisms, 1682-1873; marriages, 1682-1788 and 1792-1912; burials, 1682-1704, 1709, 1722-5, 1733-4 and 1808-1901.
There’s a copy of those records in PRONI, the public record office in Belfast. You may get their parents names from those baptism records. There are 2 other churches in the parish, both near Clones. Aghadrumsee has records for Baptisms, marriages and burials, 1829-1935. Clogh has: Baptisms, 1811-91; marriages, 1792-1910; burials, 1810-1986. Again there are copies of these records in PRONI.
Looking at Co Monaghan, the majority of Chambers there were Presbyterian. So there’s a possibility your family might have been of that denomination. If so, there’s a number of churches in the area. The only one with records for the early 1800s is Stonebridge which start in 1819. Copy in PRONI.
I looked in the tithe applotment records for Tattinbar for 1832 and there was no Chambers farm there then, so it looks as though Thomas acquired it sometime between 1832 and Griffiths Valuation in 1862.
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
John & Thomas are both listed in Roslea in the tithes so it looks as though they had farms there at that time.
I can’t help you with locating where the Chambers were buried. There’s no requirement to record where someone is buried and it’s not always the most obvious place. Some families had plots in graveyards where they used to live and so you often have to search around. Roslea is just on the border with Co. Monaghan and with some members of the family reportedly being from that county, it’s possible that there might be a burial ground in Monaghan rather than Fermanagh. You might need to ask locally in Roslea.