I searched the Irish Family History Foundation's database for Co. Armagh and surname Traynor. Rcds B4 1840 are sparse. For "Traynor" (+variants), the earliest B rcd is for 1796. For James Traynor (+variants), the earliest B rcd is 1803 and earliest M rcd is 1820.
There are 3 M rcds for "James Traynor" which correlate with your basic data. These are in: 1825, 1836, and 1838. The latter two are more probable otherwise they would have a scad of children which would need passage money.
For Mary Burns, there are M rcds for 1825, 1836, and 1838. Searching the latter two, I found there were corresponding M's for A James and A Mary in Lower Killeavy parish in 1836. These are LIKELY (but not certainly) your ancestors. You will have to view a detailed rcd to see if the two married each other. If they did, then you have validated the rcds.
It takes a while to do this type of search. Let me know of your results.