Buzzing Tube Screamer...
If you don't want to go the battery route, and have a bit of spare money lying around, get yourself a good (read: expensive) Boss dual rectified AC adapter.
One easy, visual way of seeing which AC adapter will be most silent is size within the same current rating.
ie. 9V 500mA noisy adapter will be smaller than a 9V 500mA quiet adapter.
Being in Australia, which uses 240V mains, I had to search for an AC adapter that would work with my Bad Horsie pedal (morley don't make 240V AC adapters for Oz). I went through 15 different adapters before settling on a Boss. Luckily the guy at the store let me try virtually every adapter they had there. Every other adapter (even a sony) produced more than your standard 60 cycle hum....the thing buzzed and BUZZED LOUD, overpowering the guitar.