I have no record of Charles Alderton and Frances having any children born in Suffolk. I have all the census entries for Charles and Francis, and information from the London Gazette issues 20561 and 19954 (which can be found by searching for London Gazette + Online or +archives).
The children for them that I have are born in this order between 1825 and 1842:
Edwin Adams Alderton
Alfred Adams Alderton
Frances Harriet ADELAIDE Alderton
Agnes Ann Adams Alderton
Thomas James Alderton
Amelia MARIA Alderton
Mary Ann Alderton
Frederick William Petters Alderton
It might be useful if you could explain how come you believe they had more chidlren; Charles and Caroline who were born in Suffolk and where they were staying in the censues.
Otherwise, if you can tell me when Charles and Caroline were born I can have a look for you and see if I can throw any more light.
Kind regards
Penny