from Tithes Applotment Books 1823-1837 based upon the index work of the Irish Genealogy Hub. The relevant original books are in the Public Record Office of Northern Ireland (PRONI) Belfast The record is very simple
McDonald, Peter-- Townland: Anahay Year: 1835-Killevy-Armagh
McDonald, Peter-- Townland: Anahay Year: 1835-Killyman-Armagh
McDonald, Peter-- Townland: Moorlough Yr: 1834-Galloon-Fermanagh
further tithes from
http://titheapplotmentbooks.nationalarchives.ie/searchMcdonald-Peter-Old Leighlin-Oldleighlin-Carlow-1824
Mcdonald-Peter-Dreslunan-Annagh-Cavan-1825
Mcdonald-Peter-Raskeragh-Annagh-Cavan-1825
Mcdonald-Peter-Knockategart-Larah-Cavan-1833 3 entries
Mcdonald-Peter-Aghagashlan-Drumgooland-Down-1828 2 entries
Mcdonald-Peter-Commons-Garristown-Dublin-1834
Mcdonald-Peter-Garristown-Garristown-Dublin-1834 7 entries
Mcdonald-Peter-Dungooly-Faughart-Louth-1827
Mcdonald-Peter-Moylagh,Meath-Moylagh-Meath-1826
Mcdonald-Peter-Clonfad-Clonfadforan-Westmeath-1824
Mcdonald-Peter-Monamuck-Boystown-Wicklow-1834 3 entries
So its possible he is one of these entries but equally possible he is not so do help us with any crumbs of information from his early Scottish records
those places mentioned in Durham are where Many ulster folk migrated to Durham as the Londonderry family sought extra employment for their business in mines etc in Durham etc but not in Glasgow. In particular from Co Down.
sorry cant help further.