Dear Judith, 
Going by all the Census information and the 1881 (as below) the family do not seem to have moved around much. I would assume (wrongly or rightly!) that they are present in the Llandough region in 1871. It is just a matter of finding them in the census. Which is not easy as it is not indexed like the others. You would need to know the street they were living in. Perhaps some nice person on here would do a look up for you in the area? The census addresses for your Morgan's are pretty ambiguous!
   Dwelling:   Llandough Village
   Census Place:   Llandough Juxta Cardiff, Glamorgan, Wales
   Source:   FHL Film 1342272     PRO Ref RG11    Piece 5288    Folio 105    Page 9
   Marr   Age   Sex   Birthplace
Barbara MORGAN   W   67    F   Cowbridge, Glamorgan, Wales
   Rel:   Head
   Occ:   Late Labourers Wife
James MORGAN   U   28    M   Llandough, Glamorgan, Wales
   Rel:   Son
   Occ:   Railway Platelayer
Annie ELLIS       12    F   Penarth, Glamorgan, Wales
   Rel:   Grand Daughter
   Occ:   Scholar
Glad the Census data has given you something to go on. I hope you find them in the 1871 Census soon.
Regards
Jen 
