Continuing my search for a BELLAMY and a ROTHERHAM I found a marriage entry that includes both.
Marriages September 1881
BELLAMY Sarah Ann, Sheffield
PETTY William Toyne, Sheffield
ROTHERHAM Frederick, Sheffield
SMITH Lucy Anne, Sheffield
I think I can safely assume that Sarah Ann BELLAMY and Frederick ROTHERHAM married, gave birth to a son Frederick ROTHERHAM, and the grandson was included in the England and Wales Census 1891 of his grandparents' household.
My earlier search that established a link to Richard ROTHERHAM and Frances Lily ELLIS still provides plenty of intrigue!
2005-12-15 Further research has shown this data is probably NOT linked to my family. This data may prove useful to other researchers so I will retain it.