The most quiet opener you can get will have to be a belt drive opener. The rubber belt is much quieter than a chain or screw drive opener. Also an opener that has a DC motor will be quieter than one with a conventional opener motor. Jackshaft openers do not use a belt, chain or a screw so these types are very quiet also. Liftmaster has always used a foam layer of insulation on the inside cover of their belt drive openers.

Quiet opener motor

This layer of foam helps quiet opener motor sound. As far as i know Liftmaster is the only manufacturer that uses this extra layer of noise reduction. If there is some other manufacturer that also does this Than I have not come across one yet. Most of the newer openers on the market are all equally quieter than older models now because they are all using DC motors Rather than the conventional electric motors.