For reference, here are the 7 children of John Richmond & Ellen Thompson found in LDS database (
www.familysearch.org)-
Elizabeth Richmond born 9 Aug.1864 Portglenone dist. (page 108 in civil register)
William Richmond born 18 Dec.1866 Portglenone district (page 161 in civil register)
Joseph Richmond born 21 Aug.1869 Portglenone district (page 146 in civil register)
Daniel Richmond born 17 Nov.1872 Portglenone district
Robert Richmond botn 17 Nov.1872 Portglnone district
Mary Richmond born 9 Apr.1875 Portglenone district
William Richmond born 24 Mar.1879 Portcleuone [Portglenone district]
Portglenone is the sub-registration district and may not be the actual residence of the family. Portglenone is a town (not townland) divided by the River Bann which is in both County Antrim (Ballymena registration district, Ahoghill civil parish) & Co.Londonderry (Magherafelt registration district, Tamlaght O'Crilly civil parish).
Any children born before 1864 could also have died before 1864 which will make it difficult to find details about them.
As far as 'Elizabeth born about 1867' goes- where did you find her listed. I can't see a death registration for the one born 1864 so wonder if this could be the same child.