In the 1891 census, Elizabeth Roath and children Charles, Emily and Harriet are boarding with the Turner family in Cecil Street, Birmingham. Their surname has been incorrectly transcribed as Boath (FindMyPast) and Beath (Ancestry).
Archive: RG12
Piece: 2394
Folio: 4a
Page: 8
Elizabeth is listed as a widow, so from that can assume Charles died sometime between 1881 and 1891. However, so far I haven't been able to find a death record for him either.
According to the GRO index, the following births were registered in Birmingham under surname Roath, mother's maiden name Onions:
ROATH, ELIZABETH ONIONS
GRO Reference: 1868 J Quarter in BIRMINGHAM Volume 06D Page 17
ROATH, ALICE ONIONS
GRO Reference: 1869 D Quarter in BIRMINGHAM Volume 06D Page 6
ROATH, ELLEN ONIONS
GRO Reference: 1870 D Quarter in BIRMINGHAM Volume 06D Page 33
ROATH, EMILY ONIONS
GRO Reference: 1872 M Quarter in BIRMINGHAM Volume 06D Page 31
ROATH, CHARLES FREDERICK ONIONS
GRO Reference: 1873 S Quarter in BIRMINGHAM Volume 06D Page 68
ROATH, CLARA ONIONS
GRO Reference: 1874 D Quarter in BIRMINGHAM Volume 06D Page 85
ROATH, MARY JANE ONIONS
GRO Reference: 1876 D Quarter in BIRMINGHAM Volume 06D Page 3
ROATH, ANNIE ONIONS
GRO Reference: 1878 S Quarter in BIRMINGHAM Volume 06D Page 83
ROATH, HARRIET ONIONS
GRO Reference: 1879 D Quarter in BIRMINGHAM Volume 06D Page 47
ROATH, ADA ONIONS
GRO Reference: 1881 J Quarter in BIRMINGHAM Volume 06D Page 228
So it appears they had two extra children who weren't on your original list - Annie and Ada. The following death registrations are from the GRO index:
ROATH, ANNIE 1
GRO Reference: 1880 J Quarter in ASTON Volume 06D Page 202
ROATH, ADA 1
GRO Reference: 1883 M Quarter in BIRMINGHAM Volume 06D Page 156
https://www.gro.gov.uk/gro/content/certificates/indexes_search.asp To access the index you will need to register (it's free).
It is interesting that Ada's birth was registered in the June quarter of 1881, with mother's maiden name as Onions, if Charles was by then married to Alice
It appears she is buried at Witton Cemetery in Birmingham. If you go to the following site, you can download a free index of burials at four Birmingham cemeteries and order a copy of the burial register details:
http://bmsgh-shop.org.uk/BIRM-Cemeteries