Joseph McNair immigrated in 1877 arriving in Philadelphia.There was also a Joseph McNair who arrived in Phillie in 1858.
There are two declarations of intent in Phillie records which means that the two Joseph McNairs were probably naturalized.The first was made on 1 May 1858 and the second on 4 Oct 1877.In both cases,Joseph was listed as a minor.To get copies of these contact Philadelphia Dept of Records City Archives,3101 Market St. Suite 150,Philadelphia,PA 19104.Fee is 10.00/record.Naturalizations generally have a wealth of info on them.
Next track down the marriage cert of Sarah Ann and Addison McCarrick.It may have info on the parents as well.They married about 1890.Also look for a copy of Joseph and Elizabeth's which may also have more info on it.
Joseph's death cert from 10 Aug 1941 may also have vital info as might the death cert of daughter Margaret(McNair)Drummond who died 26 May 1975 in Delaware,PA.The other Joseph McNair who died 3 June 1899 may be worth following up on as McNair isn't a very common surname in Ireland and Joseph isn't a very commonly used forename so there may be a connection between the two.On death says he was born in PA but many times in older records people but place of birth as place where people were living.He would not have applied to be naturalized if he had been born in PA.
I looked at the Tithe Applotment books 1814-1838 and most of the McNairs who were listed were concentrated in counties Mayo and Donegal.The parish registers for the parishes where McNairs are found both begin about 1850ish.Now when I looked at Griffiths Valuation only one McNair was listed in parish of Convoy in Donegal but means naught as I have found them in other places.
Firstly,you should set about getting copies of the naturalizations,marriage and death records.Those should be able to give you info to help you go back further.If I can help let me know,Kim