We have had combi boilers for over 30 years, again no noise from them when working, beyond a very slight rumble when it comes on and settles down. certainly, not the constant cycling the OP describes.
How long is your boiler on each day. We have ours on from 6.00 - 9.00 in the morning and 4.00pm to 10.00pm in the evening, so we sleep in peace at night because the boiler doesnot come on. Obviously everyones decision on the hours their boiler is on will vary, but it is not necessary to have it on 24/7.
Think about when you need heating - and also the temperature you want and insist the fitter programmes the heating system to meet your needs. When we first had CH installed in our last house we had a real tussle with the fitter over when the system went on and off and the temepratures that should be set, because the hours were shorter and the temperature a bit lower than official recommendations.