Frank,I looked at other lists and found the following for co Derry.
Griffiths Valuation 1848-1864: Alexander & Joseph in Coleraine parish co Derry John,James,Robert,Margaret & Henry in various parishes co Derry
1740 Protestant Householders List: John Harrison parish:Magherafelt barony:Loughinsholin county:Derry
will for Robert harrison who died Carrabouy,co Derry 15 June 1885
1797 Visitation Lists: Susanna & Margrat Harrison of Moneycarrie,co Derry
Rootsireland.ie has a birth cert for Charles Harrison circa 1805 but in county Antrim which is possible.
What I would do first is to check all US records working your way backwards.Census,Birth,Marriage,Death,Cemetery as they may contain vital info to narrow the search.Irish records are not very good so finding as much as you can first will be most helpful.In Ireland civil registrations of births,marriages and deaths begin in 1845 for Protestants and 1864 for catholics which isn't good for your John and Charles but you may find their parents in these.Prior to this its the parish registers which are not complete.PRONI which is the N.I. record office can be very helpful but to research their records you must go there in person.They do have some online indexes you can look at for free.If I canm help more just let me know,Kim