So sorry you and your pup are having to deal with this. My pup also has a very sensitive stomach. I did find a grain free kibble that he likes and doesn't give him the runs. in the morning I add a raw or boiled egg to his kibble and in the evening I shred up some cooked chicken with some broth and add that to the kibble for dinner. also sometimes I will add green beans or peas. Haven't had a lick of diarrhea or vomiting in three weeks.
hopefully you will find a combination that will work for you. Just be patient and don't give up.
"The more people I meet, the more I like my dog"