Hi,
I am currently in the NE program and my 'weight management' client has diverticulitis, so I had to take that into consideration when building her menu plans. I did some digging and found a very good site for info on diverticulitis and what a person with the disease should and should not eat. I also suspect that eating more alkaline pH foods would help too.
Here is a link to the site:
http://www.everydiet.org/diet/diverticulitis#diet