Is there anything in your backyard that he eats? Often it is something in their diet that doesn't agree with them. Although it can be anything from stress levels to a life threatening illness. I would get a second opinion from another vet.
Great question and a common symptom. In fact I was just cleaning up vomit from my dog Mia last night!
The first thing I do when asked this question is to determine if the dog is vomiting or regurgitating because the causes can be very different. Vomiting is an active process of heaving and abdominal contractions, often preceded by lip licking and salivating. The vomitus contains digested food often with yellow bile. Regurgitation is a passive process which commonly occurs soon after eating. Vomitus contains undigested food, often in a tubular shape due to the time it spends in the oesophagus.
So far, you have some great news. The X-rays and blood tests your vet has performed have ruled out many nasty causes! If your dog is truly vomiting, possible causes now include food allergies, inflammation of the stomach or small intestines, infections or scavenging.
If the symptom of vomiting is persisting and you're quite sure that it's not due to scavenging at the park, then a revisit to your vet is the best next step to get to the bottom of this problem. Best of luck!