Hello trudi
What denomination was Michael ? Was he a member of the Catholic faith, the Established Church (Anglicans or Church of Ireland), a Methodist or a Presbyterian?
You'll have to rely on Church records as civil registration in Ireland was not introduced until 1864. Non Catholic marriages were registered from 1845 onwards. When registration for BDMS started in 1864 some people didn't bother with the registration for a few years after that date. Keep your fingers crossed that church records still exist.
Christopher