There are no small quiet diesel generators. About the smallest is from Next Gen:
http://www.nextgenerationpower.com/
Their smallest gets 3500 watts out of a Kubota single-cylinder diesel.
It's impressively efficient - 0.2 gallons per hour of fuel (on a watts per gallon basis, that's like 17,000 watts per gallon, compared to a Honda inverter which gets like 4,000 watts per gallon at its most efficient).
But according to those who've experienced it, it's also impressively noisy.
Also costs around 5 grand.
I've seen some Chinese small diesel generators advertised. I know nothing about them, but I would assume they are noisy.
That would be a waste - if you are running a generator anyway, you might as well charge the battery at the same time.
But whether the solar/battery setup would be enough for "everything except a/c" depends on how much solar and battery you have, and what the loads are on it.