You don’t say what denomination the couple were but I’ll assume RC. If so, a marriage in 1859 won’t be in the statutory records. (RC marriages were only recorded there from 1864 onwards). You will therefore need to search church records for it. About half of the 30 or so parishes in Co. Tyrone are on rootsireland (subscription). Alternatively a more complete set of RC parish records are on the NLI site (free to view) but unless you know which parish your ancestors came from, you may have to work your way through up to 30 sets of records to find it.
http://registers.nli.ie/parishes
Don’t expect too much information from the entry if you find it. Most RC marriage records from that period just contained the couples names, the date and their 2 witnesses.