In the beginning...
Jonny Quest started Friday, Sept. 18, 1964, at 7:30 p.m. Eastern then moved to Thursday evenings at 7:30 starting Dec. 24, 1964, switching timeslots with "The Flintstones."

Current
It just depends. The only channel that I know of it being on is Boomerang. It's typically on everynight, but sometimes they change things around. That's just a cartoon network thing, though...

here are some links that will help you: Boomerang | 1964 | Schedule