I am sorry to hear that Bongo has had stomach rouble for the past 2 weeks, vomiting slimy green mucous almost daily.
I am glad to hear that he is producing normal feces and he is still active.
I understand that his appetite on and off. When he eats does he eat a full meal?
I understand that his physical examination was within normal limits.
Did your veterinarian perform any testing (blood tests, radiographs)?
Were any medications prescribed, and if so what were they? Did they help at all?
Dogs that have a gastrointestinal blockage or very abnormal intestinal motility often vomit green material as that is digested bile, bile that sits in the stomach for a while. Bile only refluxes back into the stomach when gastrointestinal motility is abnormal, such as with a blockage or poor gastrointestinal motility due to primary intestinal or metabolic (liver) disease.
Vomiting can be related to chronic pancreatitis, a dietary allergy or sensitivity, toxin exposure, a viral or bacterial infection, inflammatory bowel disease, internal organ failure, a full or partial gastrointestinal obstruction or even infiltrative cancers such as lymphoma.
Is he a fellow that gets outdoors unsupervised such that he could get into something you don't know about?
Or is he a fellow that eats things like rubber bands, toys other things he should not?
Because his appetite isn't normal and he is vomiting repeatedly I am very concerned about him. He will quickly become dehydrated and will start to lose weight.
Ideally because his symptoms are persisting he would see his veterinarian again for diagnostic testing. Simple stomach upset should pass within 24 to 48 hours. They could re-examine him, run blood tests and possibly check radiographs and/or an ultrasound to evaluate him and know best how to treat him. I would start with a complete blood count, biochemistry profile, can spec PL (canine specific pancreatic lipase) and abdominal radiographs.
In the meantime they can administer injectable anti-nausea drugs and fluids to rehydrate him.
If you cannot have him seen for whatever reason there are some things you can try at home, though if he doesn't respond quickly he should see a veterinarian again.
At home to try and settle his stomach you can give either:
1) Pepcid ac (famotidine) at a dose of 1/2 of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours
2) Prilosec (omeprazole) at a dose of ¼ of a 20mg tablet per 10 to 20 pounds of body weight every 24 hours
These are acid reducers and may help him feel better. They are quite safe and can be used for several days if necessary.
A couple of hours after giving the acid reducer I recommend offering soft foods mixed with water to make eating and swallowing more comfortable.
If he is refusing to eat even soft foods you can try offering meat baby foods or a bland diet mix of 1/3 boiled, minced, white, skinless chicken or boiled, very lean ground beef, and 2/3 boiled white rice mixed with some low salt chicken broth to make it easy to lap up and swallow.
If Bongo continues to not eat normally and vomit green material he should see her veterinarian or an emergency veterinarian for an examination, diagnostics and intravenous fluids and supportive care.
Please let me know if you have any further questions.