An Airbus service operates every 30 minutes, Monday to Saturday, between Belfast International Airport and the Europa Buscentre in Belfast, and at 30 or 60 minute intervals on a Sunday. The service operates between 05:45 and 23:20. The journey from the airport to Belfast takes about 30 minutes.
The Ulsterbus express bus between Belfast Europa Buscentre and Armagh takes about 1 hour. Avoid the regular service which takes the pretty route, stops everywhere and takes a long time. It is possible to take a bus from Dublin Airport to Newry and then take a taxi to Armagh.
Northern Ireland Railways operate an express service between Belfast and Dublin, stopping at Portadown. Portadown Station is ~10 miles from Armagh. It is advisable to take a taxi from Portdown to Armagh as there are limited buses available.