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