I think that you all may be speaking about the following family---if I have read this correctly. Please respond if this is the family that you search!
1880 USFedCensus MO,DouglasCo.,JacksonTwp.,EnDist30 enumerated 21 Jun 1880 by John Wheat Ln5 266/274 ALEXANDER, Wm wm56<1824>head FmgNC NC NC Alexander,Nancy wf42<1838>wife KpHs KY KY KY Alexander,William wm 22<1858>son WksOnFm KY NC KY Alexander,Catherine wf 19<1861>dau WksOnFm KY NC KY Alexander,James wm 17<1863>son WksOnFm KY NC KY Alexander,Job wm 15<1865>son WksOnFm KY NC KY Alexander,Benjamin wm 14<1866>son WksOnFm KY NC KY Alexander,Mary wf 13<1867>dau WksOnFmKY NC KY Alexander,Silas wm 10<1870>son WksOnFm KY NC KY Alexander,Margaret wf 8<1872>dauKY NC KY Alexander,Martha wf 2<1878>dauKY NC KY
Earlier family I believe may be this one. 1870 USFedCensusKY,GraysonCo.,CaneyPrecinct Post Off: Caneyville,KYenumerated 9Jul1870 byPSBarnes? Ln20187/187 Alexander, W.P.(?J)45<1825>mw Lbr 0/200 NC Alexander,Nancy35<1835>fw KpHsKY Alexander,Darrell18<1852>mw LbrKY Alexander,William16<1854>mw LbrKY Alexander,Permelia 14<1856>fw AtHmKY Alexander,S.(?D)C. 12<1858>fw AtHmKY Alexander,James10<1860>mwKY Alexander,Job8<1862>mwKY Alexander,Benjamin5<1865>mwKY Alexander,M.C.4<1866>fwKY Alexander,Silas1<1869>mwKY Ln 31188/188 James, James64<1806>mw Lbr 0/120 KY James,M.C.59<1811>fw KpHsNC
I had assumed that the female child (12 y)above is your Deliah Cathrine and that the younger female may be Mary Cathrine (4 y) above may be named after their grandmother presumed to be the James, M.C. next door.