I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840. Rare B4 1800.
For Sarah Cumisky, the earliest M rcd in all Ireland is for 1866 in Co. Down.
For Grace Crozier, there are 0 M rcds in all Ireland.
For James Davison B 1797 +/- 4 yrs in all Ireland, I found 2 B rcds: 1795 and 1798, both in Antrim.
For Henry Davison B 1832 ditto, I found 0 B rcds.
For Sarah Davison B 1835 ditto, I found 4 B rcds: 1835 Antrim, 1836 Antrim, 1837 Armagh, and 1839 Antrim.
For Grace Davison B 1840 ditto, I found 0 B rcds.
For Mary Davison B 1827 ditto, I found 13 B rcds.
Because I find rcds for some of the children, but not the others, I conclude that NONE of these are likely for your ancestors.
For the Scottish connection, I suggest you search the English censuses. There was temporary seasonal migration from Ireland to England/Scotland for harvest. There was emigration during and after the famine to escape the poverty and starvation in Ireland. The fare from Ireland to England/Scotland was abt 1 shilling. Emigrants went to nearly all the major ports on the west coast.
Google the Foundation's name to lead you to this database. Pls post your search results to this genforum msg.