Statutory recording of births only started in Ireland in 1864 so you won't get a birth certificate for Neal. You'll have to rely on any baptism record, if it has survived. (Irish records are patchy). You'll need to establish his religion and ideally his townland or exact parish in Ballintra. Some parish records have been copied and are in the National Library in Dublin. Others are still held by parishes. It depends.
Stat recording of all marriages was in place by 1864 so for a marriage in 1866 you should be able to find a certificate. You can search on the LDS site, or if you have full details get a research copy of the marriage cert from the GRO in Roscommon.
Elwyn