The best you can do (while not blowing your wallet) is to use the good old egg cartons, from pirate radios from decades ago to this day it still remains an incredibly solid method to disperse sound waves and effectively making the whole thing a lot quieter!
Unfortunately this doesn't work. Egg crates will result in attenuation of some higher frequenies, which can knock down some of the 'snap' or 'sharpness' in a room. This is why it had limited use in the radio / spoken word application. However, egg crate is totally ineffective in reduction beyond a couple of decibels, which Is trivial. Sound reduction Is acccomplished through absorption, which requires either mass or isolation. There are no shortcuts.
Edit-- don't want to post just a negative thread, so adding some hopefully productive input: Resinlip is already onto a potential solution, which is to decouple the regulator making the noise from the tank which is magnifying it. That is the proper direction; to address the noise at the source. The ping is a high pitch, which is also easier to damp. He could additionally dcouple the tank from the floor, or damp the tank as well, as it's also producting noise. The other option is to look at where the noise is transmitting out into the house-- direct propogation of waves though the door, as well as possible indirect transmission though the walls and floor. This would show where to apply any absorptive treatment.
