An inexpensive way to decrease any noise source like this is to make the sound turn 90°. For example, I have an old small CH single hot-dog oilless compressor. It's not near as loud as a neighbors small pancake that runs at a much higher rpm, BUT it can still be a bit much when frequently used AND it's inside the garage with me when I'm working.
During a recent project, I took it outside the garage side door and placed it a few feet away, along an outside garage wall. I slid the hose through the doorway, then closed the door. The main garage door was still open. To reach this opening, the sound would have to travel two 90° angles. As an experiment, I opened the smaller door. It was still rather quiet. Once you walked out the door where you could see it though, it was much louder.
Fein uses this technique with their shop vacs. They use a foam-lined hood to dampen the higher frequencies of the fan exhaust and blow it straight down at the ground around the perimeter of the hood.
So when you're using it and it frequently comes on, take it outside, turn at least one 90° corner and set it down. Since sound level falls off as the inverse square of the distance, you'll also have this fact work with you. Between both of them, it will result in a significant reduction in noise. You may need another 50' of hose, but that's not too expensive.
Yes, belt drive, oil-compressors are quieter.