What's the rationale behind eliminating vinegar? That will help me a whole lot in suggesting alternatives.
If it's the acids, you're SOL. If it's a specific acid, we might be able to work here.
Acetic acid: most vinegars are this
Citric acid: fruits, but also tomatoes
Lactic Acid: soured milk products
Malic acid: strawberries i guess
If they cant tell you which of these or why, then you can figure out what is safe. If it's the bacteria the create acids, there's another consideration. Acetobacter and lactic acid bacteria can be very helpful, and are usually suggested as things to reduce allergies or other odd symptoms, but who knows, maybe they can cause problems sometimes. If they can't tell you more, then nothing sour is going to be a good idea while you're doing the initial stage.