If you will be living in Northern Ireland and not the Republic of Ireland, then you won't be able to apply for a 4EUFAM visa - because that visa is only for people who live in the Republic of Ireland.
If your wife is an Irish citizen living in Northern Ireland, then you would need to apply for a UK visa, not an Irish visa, in order to live and work in Northern Ireland.
If she is an Irish citizen only and does not hold a UK passport, then you should be able to apply for an EEA Family Permit to live and work in Northern Ireland with your wife. The permit is free of charge and is valid for 6 months, but it only allows you to live in Northern Ireland (or the rest of the UK). If you wished to live and work in the Republic of Ireland (but not Northern Ireland), you would need to apply for the 4EUFAM from Irish immigration.
You would use the EEA family permit to enter Northern Ireland as the spouse of an EEA citizen, and then once you have moved, you will need to apply for a 5-year EEA Residence card (also free of charge) to show you have permission to live there for 5 years.
See here for more information:
http://www.ukba.homeoffice.gov.uk/eucitizens/eea-family-permit/