Welcome to Rootschat. Looks like they moved to Scotland just after the marriage-
Children of William Crichton and Jane Nelson (
www.familysearch.org)-
1. John born 10 Apr.1856 Old Cumnock, Ayr, Scotland
2. Jane born 28 Feb.1858 Tradeston, Glasgow, Lanark, Scotland
3. Isabella born 3 Oct.1860 Central District, Glasgow, Lanark, Scotland
Then perhaps came back to Ireland? as there's also this entry:
Mary Elizabeth born 1 Feb.1869 Co. Down, Ireland
Civil registration of Catholic marriages began in 1864 but registration of other marriages from 1845 so if William and Jane weren't married in a Catholic church you should be able to find their marriage in civil registration index. Search for bride and groom separately then cross-reference results for match and then you can order the cetificate. Warning- Irish civil marriage certificates only contain the following details: date, place and name of officiant, name, marital status, whether or not of full age, residences (at time of marriage),
occupation, father's name and occupation, names of 2 witnesses.
http://pilot.familysearch.org/recordsearch/start.html#p=collectionDetails;t=searchable;c=1408347