Hello AB I had a quick look at some records, checked a few parishes in the diocese of Raphoe and earliest records only started in 1850 and much later for RC parishes, did not look at tthem all but you can click on the map on this site and see when the various parish records are available https://registers.nli.ie/
I checked the subscription site Roots Ireland 1820 to 1840 and got two hits, one Kergan is Church of Ireland (Protestant) and one Susan Carigan (spelling) in Bogstown, Moville in October 1834, mother Wilson father Hugh.
I looked in the Tithe Applottments for those holiding over 1 Acre of land for tax purposes and got about 4 different Carrigans and many Kerrigans, no Corrigans, this is only the name of one person but shows where they are, the site I do not think gives variant spellings of names. See http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp the period is 1824 to 1838 I think.
It appears any baptism registers in Donegal were either not kept or are missing.
Griffiths Valuation done circa 1858 for Donegal lists 3 Carrigan, some Corrigan and 126 or so Kerrigan, see https://askaboutireland.ie/griffith-valuation/index.xml?action=nameSear…;
I think there were sailings from Donegal possibly Ballyshannon at some point to the US and Canada, a visit to the Donegal Library site may be benefical to see what local studies have and you could email a query. https://www.donegalcoco.ie/culture/archives/familyhistory/
Good Luck
Pat