cheap = noisy, expensive = =quiet.
Much of the noise on a small air-cooled engine comes from the cooling fins and there isn't a lot you can do about that. If you really need quiet, look for a generator built for RV usage. Most of them run at 1800 RPM verses 3600 for the inexpensive ones and are designed from the beginning with quiet in mind. They will also outlast the cheaper units by several times. New ones are pretty pricey but used and takeouts can be has for a lot less. Check a local RV junkyard.
You can add a bigger muffler to the original and soften the bark a bit but it won't help all the other noise it makes.