I searched the Irish Family History Foundation's database for Cavan.
I found 2 M rcds for John Tuite in Cavan in 1858 and 1859; however, for Katherine Bennett, I couldn't find a marriage rcd in Cavan in a relevant year. It could be she wasn't a local girl. This would infer a marriage elsewhere. But, I can't find a John Tuite M outside Cavan in a relevant yr.
For John Tuite, I found 1 1869 B rcd in Crosserlough. There is a B rcd in 1861 for Patrick Tuite in Castlerahan. Mary 1864, Hugh 1867, Cornelius 1871, Hugh 1871, Rose 1872, and Thomas 1875. Will let you find the parish(es) for the other children.
Will let you google the Foundation's name and browse the database.