There are numerous examples of solid murder convictions for cases in which the body is not found.
There was a guy in Florida about 5 or 6 years ago, who moved into a girlfriend's trailer with her and her little daughter. I think his name was Crane or Crain. Something like that. Anyway, the girl went missing about the same time he did. No body, no witnesses, no confession. But he was given the death penalty by a jury who saw lots of strong forensic evidence of a violent episode involving the defendant and the girl.
But no matter how much evidence there is, some people are never convinced. They'd have to see it with their own eyes and even then, they would doubt what they saw. Some of them just like to argue to the point of absurdity.
There have been a number of murder cases with convictions and no body. I can't remember the names of any of them, but do remember seeing some of them on "The New Detectives", and reading about a couple of them in books by Ann Rule. There was one case I recall where there was no body, but the medical examiner was able to determine by the amount of blood found on the carpet pad and floor under the pad (carpet had been discarded, and another one placed over it, if I recall) that no one could have lost that much blood and survived. A case that Ann Rule (true crime writer) wrote about, there wasn't even any blood found. It was a completely circumstantial case where a wife had disappeared, and the husband's lies and bizarre behavior were enough for the prosecutor to put a case together and get a conviction.