Marriage of Arthur Timmins and Elizabeth McCaffrey, Arthur's age is inconsistent, but I think it's the same person:
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1862/09626/5491106.pdf
Just to say up front that the name Arthur Timmons (and surname spelling variants) is very rare - you can check so yourself in the likes of the 1901 and 1911 Ireland censuses.
Arthur's address in the above 1862 marriage registration was Portlongfield townland in the civil parish of Killashandra, his father recorded as also being called Arthur. The tithe applotment books show an Arthur Timmons in Portlongfield townland (1832):
http://titheapplotmentbooks.nationalarchives.ie/reels/tab//004625671/004625671_00181.pdfGriffith's Valuation has a print year of 1857 for the local area and while there are Timmins in Portlongfield, the only Arthur goes by the surname Timmin, living in the townland of Dunaweel, which is the immediate townland neighbour of Portlongfield.
One of the relatively few surviving Irish census fragments for 1841 shows a farmer called Arter Timmon living in the townland of Donawell (Dunaweel) in the parish of Killashandra, on the first page/side, it has a section for all people in the household who died since 1831, under which it shows a 70 year old brother John Timmon, who died of 'Decline' in 1839:
http://www.census.nationalarchives.ie/reels/c19/007246502/007246502_00195.pdfOn the second page/side, it shows everyone in the household on the night of 6 June 1841 - 60 year old Arter Timon and his wife Mary of the same age - who married in 1826 - 4 year old grandchild Patt Rielly, 28 year old daughter Jane Timon, 28 year old son Patt Timon, 17 year old son Arter Timon and 15 year old daughter Fannay Timon:
http://www.census.nationalarchives.ie/reels/c19/007246502/007246502_00196.pdfThe marriage year and older childrens' ages (if correct) would suggest that Mary wasn't Arter's first wife.