I think "somewhere between Charles and Henrietta" is as good as it gets!

The problem lies in the ambiguity of birth dates being inferred from ages. At the time of the action of the novel in September 1814 Louisa is said to be "twenty". This could mean she had just had her 20th birthday which would put her date of birth c. August 1794, or she might be almost 21 in which case she was born c. October 1793. The same applies to Louisa who was born 1794-1795.

More ambiguity lies in determining Dick's age and date of death, which occurred "before he reached his twentieth year". His twentieth year was the year during which we would say he was 19 years old, (think about it - you have to include the first year of his life), so I take this to mean that he was 18 when he died. His death happened "two years ago" plus the time it took for the news to reach Uppercross. This probably places his death in 1812 but it could well have been earlier - if Dick was on a long voyage (eg to the Far East) it could take a very long time indeed for the news to work it's way back to Uppercross.

With all these ambiguities I can just about fit Dick's birth in between Louisa's and Henrietta's, but think it more likely that he was older than Louisa, though not by much.