Brian Muehl: 1978(?)-1984 (however, I've read that Brian Muehl was credited with performing Barkly in the 1987 special Big Bird in Japan, though Muehl had stopped performing on Sesame Street in 1984, and Fred Garbo Garver had already been performing Barkly, the earliest known proof of him performing Barkly being the 1985 movie Follow That Bird)
Fred Garbo Garver: 1984-? (his last known performance as Barkly that I know of was the 1989 special Sesame Street: 20 and Still Counting)
Bruce Connelly: ?-present (?)
Toby Towsen also performed Barkly in A Special Sesame Street Christmas (I've heard that the costume was much bigger in that special). I don't know if there were ever any other performers performing Barkly whenever his regular performers either weren't available or performing other characters of theirs who spoke in scenes with Barkly (though I believe that Brian Muehl was the only Barkly performer to actually have other character sof his own).