The reigns of Charles II and James II were from 1660 to 1690 (when James abdicated). So that probably dates their move to Raphoe (current spelling) which is a parish mostly in Donegal. It was certainly heavily settled by Scots, most of whom were Presbyterian) something you may need to know if searching church records).
Hardly any records at all survive from that period. Occasionally you find some records of the major land owners who settled in Ireland. (But there are none for any sub-tenants who chose to accompany them). You could try searching in PRONI, Belfast (the public record office). They have an on-line e-catalogue. Search under the various spellings of the name plus Raphoe to see what comes up.
The documents themselves are not on-line (being all in paper format, and deposited there by the big estates) but if you see something that looks promising then let me know. I live near Belfast and can look them up for you if needs be. The records are free to access.
The sort of documents you might find are leases, legal disputes etc.
Likewise you could search the National Archives in Edinburgh for references to Harrises of Lochcandiloch. (I am away in Spain at present, otherwise I´d look for you).