Attached newspaper article in 1812 suggests the Maghera Brewery was in Belfast, not Maghera Co Derry.
There are no passenger lists for journeys to Greenock. That was (and still is) just a short domestic journey. Belfast to Greenock is probably 100 miles and would have taken 5 or 6 hours in those days. Fares were low and folk went back and forth all the time (as they still do).
Likewise there will be no departure records from Greenock. The authorities had little interest in who was leaving and whilst a passenger manifest was probably produced on arrival in Australia there was normally no paperwork kept in Scotland (or Ireland) for folk leaving.
Statutory recording of births started in Ireland in 1864, and protestant marriages were recorded from 1845. So your couple were born and married before those dates. We rely on church baptism and marriage records for those earlier events but you need to know where and when they took place to try and trace them. Some are on-line but many are not. If you think they may have married in Belfast (as seems possible) then you could get a researcher to go through the Presbyterian and Church of Ireland records for the city (probably 30 relevant churches). They are kept in PRONI, Belfast.
Try the rootsireland site (subscription) as they have some Belfast records on-line. Bear in mind that tradition was to marry in the bride’s church so though Robert was Presbyterian, his bride may have been another denomination (Church of Ireland/Baptist/Methodist etc).
Being Presbyterian and living in Ulster generally points to Scottish roots. (The Scots brought Presbyterianism to Ireland). So his ancestors probably came from Scotland in the 1600s. (Some 200,000 Scots settled in Ireland in that century, mostly in Ulster).