If your compressor already has a two gallon tank why not simply put it outside and run a hose into the basement, or run it when the baby isn't home to fill it, then shut off the switch and use the air in the tank?

You could also build a simple enclosure around it and insulate it well to reduce the noise. I have a huge, industrial grade stand up air compressor at my shop that is very loud and I did just that. I built a small 'room' around it, insulated the walls and now you can hear yourself think when it kicks on.

As has been said, those compressed air cans suck and unless you are a traveling salesmen who wants to pull the can from his suitcase and spray in his hotel room, I see no real use for them.