Have you got some DATE references. I've looked through a bmd data bases and found no listing of children for Henry Dawson and Betsy Donaldson in Cavan. Did a wider search of Ireland in general with the same result. These would be
1900 and prior?
One baptism for Henry Dawson in Cavan in 1811?
Dawson doesn't appear to be a common name in Ireland in General although in the 1911 Census there are 32 Henry Dawson of various ages. None in Cavan.www.nationalarchives.ie
A lot of the farmers in Cavan were Scots in origin, I did a search for a friend whose grandfather born in Cootehill came to Canada, his parents went back to Scotland.www.familysearch.org
bmd for 1864+ for Ireland, this is an international website. The IGI records for Scotland are extremely good but this was a search for a birth record for James Dawson in Cavan:
James born 06 Oct. 1816, father: Samuel Dawson & Susanna
James Alexander Dawson Jan-Mar 1940 Cavan
James born 1889 Lurgan, Armagh
James born 1907 Lurgan, Armagh
Henry Dawson born 20 Jan 1880 Billis, Cavan father: John
Dawson and mother Mary Anne Candler
there are 4 other Lurgan births, 1 a Henry 1903.