You've got three main issues to consider. One is where it contacts the floor. A firm mounting point can help reduce the vibration. You don't want to bolt it down due to tile. Maybe you can bolt it to a large board and use some type of removable adhesive to hold the board to the tile.
The second issue is your plumbing transmitting the vibrations to other surfaces. Those vibrations can actually be amplified, sort of like how a small magnet makes a load sound with the cone of a speaker. Securing your plumbing firmly and using a flexible section of pipe, such as flexible PVC, spaflex, or silicone tube, near the pump to dampen the transmission of the vibrations along your plumbing can help.
Perhaps your stand is acting like a speaker box. Some foam might help with that.
Well, I guess your pump could be broken or dirty too. It might be worth opening it up just to make sure it's clean and in one piece, but it's probably fine.
