Hey Missy the only thing I can think of is what I did when you kids were babies - I put a small lid - like the top of a pump hairspray bottle - over the buzzer and duct taped it down. Then, people have to knock. Could you do something like this? Then hang a little wreath over it and a cute "please knock" sign or doorknob hanger. Or, if you can find the doorbell unit in the house, you might be able to put something in the casing (styrofoam or insulation) to muffle the sound if it is the vibrating type. Poor Boomer - this must really scare him to run and hide like that!!
Hope this helps!!