As Aghadowey suggests your first port of call would have to be the marriage certificate. Here are the marriage details from EmeraldAncestors.com subscription site:-
Date of Marriage 4 May 1847
Groom Name William BUCHANAN
Bride Name Matilda CARSON
Church Crew Bridge Church of Ireland
Parish Ardstraw
Civil District Castlederg
County Tyrone
The certificate will give addresses and father's names for the bride and groom which will enable you to connect your couple to a wider Irish family.
Details from marriage certificates are available from most Northern Irish district councils for around £4 provided you have the name of the bride and groom and the exact date and place of the ceremony (as provided by Emerald above). The relevant council in this case is Strabane and their district registrar can be contacted by phone or email via the following link:-
http://www.strabanedc.com/council/services/births-deaths-marriages-and-civil-partnerships/Once you have these details, post them here and someone should be able to help.
A good place to start would be Griffith Valuation which would give details of where their families lived:-
http://griffiths.askaboutireland.ie/gv4/gv_family_search_form.phpbut you need addresses and father's names as a starting point (a quick check of Griffith shows 11 Carson families in Ardstraw parish in 1860).
Good luck