Carndonagh is in the RC parish of Donagh. Unfortunately their baptism and marriage records only start in 1847, so you are not going to find William’s baptism for his parents marriage (assuming they married in that parish) from that source.
I have searched on the Irish civil indexes for deaths for William & Ann Crosby/Crosbie in Inishowen 1864 – 1900 but there are none listed. That might suggest both died before 1864. There are however a few births and marriages listed, so the name was certainly found in that area OK.
There were a couple of William Crosbies who lived in Ramelton. One died 25.3.1894, the other 5.6.1905. Both had probate files.
http://www.willcalendars.nationalarchives.ieLooking at the 1901 census for Co Donegal there are only 11 Crosbie names listed. All were either Church of Ireland or Presbyterian, save for 1 RC who was the local Magistrate, and he was born in Scotland. So I wouldn’t be too certain that your family were RC. None of the Crosbies on the 1901 census lived particularly close to Carndonagh.
Carndonagh Presbyterian records start in 1830 and are on-line on the rootsireland site. However there are no Crosbies listed. The local Church of Ireland’s records were lost in the 1922 fire, so no joy there either.
