I found William but not Frederick .....

William COOPER
Birth - 27 JAN 1808
Christening - 26 FEB 1808
Saint Mary-St Marylebone Road, Saint Marylebone, London
Father - William COOPER
Mother - Elizth
And Elizabeth ...
Elizabeth COOPER
Birth - 04 JAN 1810
Christening - 04 FEB 1810
Saint Mary-St Marylebone Road, Saint Marylebone, London
Father - William COOPER
Mother - Elizabeth
And Charles
Charles COOPER
Birth - 11 FEB 1814
Christening - 06 MAR 1814
Saint Mary-St Marylebone Road, Saint Marylebone, London, England
Father - William COOPER
Mother - Elizabeth