Try singing or humming. Certain music may work as well. Play nature tapes. Sounds of the ocean or rain forest can have a calming effect. Sit your child in a baby seat while the running the washer.
Some children relax from the motion of a washing machine in use.
Run the vacuum claner. The constant hum typically has a lulling effect. The blow dryer may also be effective. Make a tape of the sound that works, so you don't have to pull out the appliance to quiet your baby.