Alternatives include DIY boxes with any material which would serve as a muffler - high density cloth, dense closed-cell foam and so on. Simply wrapping a camera in thick towel also helps.
Check if your camera body has a 'silent' shooting mode, usually it will be a delayed mirror return arrangement, or an option in Live View.
Other options include choosing cameras with no mirror - P&S, compacts, prosumers and film rangefinders.