Tradition was to marry in the bride’s church. Have you searched St Columbs records for Eleanor’s baptism (and that of any siblings)? Their records go back to 1642.
I looked at Slater’s Directory 1846. It lists 5 bookbinders in Derry but none named McLeary:
Likewise in 1824:
The 1831 census has several James McLeary/McCleary/McCleery entries but none in Derry itself.
Something to bear in mind was that if this was a mixed marriage (as your Tyrone post states), Eleanor may not have been brought up Church of Ireland. She may have been Presbyterian (a lot of the population in that area were, being descendants of Scots who arrived in the 1600s). In 1839 neither the RC nor Presbyterian churches routinely married mixed denomination couples, whereas the Church of Ireland would marry anyone. So until the law was changed in 1845, a lot of mixed denomination couples used the Church of Ireland even though neither of them was of that denomination themselves. So probably worth checking the Presbyterian baptism records for Derry, if you don’t find Eleanor in the COI records.
Note that Eleanor may appear in records as Ellen, which was very popular in Ireland.