The births are long before the start of statutory birth registration in Ireland (1864) and so you won?t get birth certificates. You?ll have to rely on church records. You don?t say what denomination the family were. Drumboarty is in the parish of Drumkeeran. The townland is about a mile from Ederney. Assuming they were Church of Ireland the parish records start in 1801 so there?s a fair chance you?ll find them. The records don?t appear to be on-line anywhere. However a copy is held in PRONI (the public record office) in Belfast. If you can get there, or get someone else to go for you, then you can research them. They are on microfilm.
Alternatively you can write to the Rector or Vicar at Drumkeeran parish church but the Church of Ireland does charge for researching their records. If the Rector agrees to do the work, he may charge ?19 an hour. You would need to confirm that with him/her.
Griffiths Valuation for 1862 has John, Henry & Robert BAKEHAM listed in the townland (plots 1, 5 & 6) so that?s another spelling to look out for. And clearly they are likely to be related to your ancestors. There were only 9 farms in the whole townland and the Bakehams had 3 of them. Plot 5 was still in the family?s hands in 1929 when it was occupied by John Beacome, according to the revaluation records.
http://applications.proni.gov.uk/dcal_proni_val12b/RelatedVolume.aspx?9…
There were 2 Beacom farms in Drumboarty in 1901:
http://www.census.nationalarchives.ie/pages/1901/Fermanagh/Tirmacspird/Drumboarty/
and 1 in 1911:
http://www.census.nationalarchives.ie/pages/1911/Fermanagh/Tirmacspird/Drumboarty/
I can?t see any Beacom households in Drumboarty at present but there?s 3 or 4 in Kesh a few miles away in the current phone book. http://www.ukphonebook.com