There are several ways to make a motor quieter-
1. Use sound dampeners- they go under the engines outer covers- sometimes even over the motor if there's enought crank clearance- you can get themm from vendors here for about $15 or make them yourself, using the covers themselves as a tracing pattern-
some people use just cardboard- I've used styrofoam-
here's some of my old videos about it:
Installing sound dampeners
http://www.youtube.com/watch?v=GUZcD5Cpe2I&list=UUOcL4qNa1PxaUzgfjeERryg&index=3
50cc vs. 66cc sound comparison
http://www.youtube.com/watch?v=k3ejWhPVZaY&list=UUOcL4qNa1PxaUzgfjeERryg&index=2
2. You can add length onto the muffler- a long poo poo pipe is a bit quieter than the stock pipe- several other types in between- try Gasbikes
3. You can put on a larger gear (smaller back sprocket i.e. 36 teeth) which makes the motor relatively less quiet and less vibration- because you run at a faster cruising speed at fewer RPM and that can really make a difference
As far as the frame- generally womens frames are harder to motor, so use a man's frame if you can- I like a modern cruiser frame for motor and gas tank clearance- it's a bit laidback so you're not leaning awkwardly too far forward at higher speed- BMX or high rise bars help there too- but a lot of people do use diamond mountain bike frames.