I’ve had an idle hour Googling today and found a few things that might be of use if you don’t already have them.
There are two letters mentioned in the catalogue of the library of Harvard University: a letter (scroll down to 164) from Richard Cumberland to Sir James Bland Burgess, written in 1801
‘with comments on the death of Edward Riou and other current events'.
http://oasis.lib.harvard.edu/oasis/deliver/~hou01762
and a letter
written by Edward Riou to Charles Saxton (Scroll down to 153d)
http://oasis.lib.harvard.edu/oasis/deliver/~hou00364
The Harvard Library staff are enormously helpful and courteous. I have had dealings with them in the past. If you contact them by email they will arrange photocopies of the letters and post them to you without charge.
There is also an interesting article in the Daily Telegraph about the sale of a miniature of Riou and some biographical detail. Treat this with caution, though – journalists often get their facts confused! And don't read this if you are a dog lover.
http://www.telegraph.co.uk/news/uknews/ ... a-dog.html