I am assuming that the Deputy is referring to non-EEA nationals who have applied to come to Ireland or remain here by virtue of being a spouse or partner of an Irish national and not by any other basis.
I am advised by the Irish Naturalisation and Immigration Service (INIS) of my Department that immediate family members of Irish citizens who apply and are granted immigration status by INIS through the family reunification process have the right to work without employment permits and to establish or manage/operate a business in the State. They should receive a "stamp 4" immigration permission.
Further details of the relevant Domestic Residence Schemes can be found on the INIS website under the heading of ‘Family, spouses & partners’ at: http://www.inis.gov.ie/en/INIS/Pages/immigration-permissions
If the Deputy has any other category of person in mind or has a specific case in mind I would be happy to respond with relevant details.