Robert Colquhoun

Statutory birth registration only started in Ireland in 1864, so you won’t find a birth certificate for someone born in 1845. Prior to that you need to rely on church baptism records, where they survive.

You don’t say what denomination James was. Do you know?

Looking at the 1901 census for Donegal there are just 15 Colquhoun entries, mostly Church of Ireland. Just a handful of families. The spelling of the surname may have changed. Colquhoun is more common in Scotland. In Ireland the most common is Colhoun and there are 207 of them in the 1901 census for Donegal. (16 named Robert).  Most are Presbyterian, pointing to Scottish ancestry. Not surprising with such a Scottish surname. And Co. Donegal was heavily settled by Scots at the time of the Ulster Plantation. So that fits.

If you don’t know where in Donegal Robert originated, you would really need to work your way through all the surviving Presbyterian Church records. And perhaps the Church of Ireland too. That’s quite a lot of records. Not all are on-line. The most complete set is in PRONI, the public record office, in Belfast. Their copies are not on-line and so a personal visit is required to access them. If you are unable to go there yourself, you may need to employ a researcher.

http://www.proni.gov.uk/guide_to_church_records.pdf

Ideally you need Robert’s father’s name to ensure you find the correct baptism. You might get that from a marriage or death certificate.