you will probably need a bit more detail to start a search - e.g. where was the son born ? where did Stephen and Elizabeth get married ?, where did they live later etc ?
Might be an idea to follow up on later records of the couple, e.g. death certs, to try to work out approximately when they were born. Depending on where they ended up death certs may also give details of parents... Also their marriage cert - usually would give father's names at least
Your dates are well after the available census, and also after most of the Irish online parish records, so any births or marriages will require a search of the BMD Index (which is on FamilySearch), and ordering certs to see if the details match up with your clues.
Crowe or Crouse would be the less common surname, so I'd suggest focusing on these as there should be fewer results to check out.
see :
Introduction to Irish Records