Which light aircraft are known to have a quiet cockpit?
I assume that you're asking about piston engine light aircraft, so we can ignore gliders and electric engines for now.

The basic point is that they're all loud. One study compared a Cessna 172 (single engine) and a Piper Seminole (twin engine) and found that the average cabin noise was around 86 decibels, with no huge difference between the two aircraft. There's more analysis of a Seminole here. The FAA says that a light aircraft cabin is in the range of 70-90dB and this Cirrus owner measured 92-98dB in different Cirrus models. OSHA in the US requires ear protection and other measures for workers if the noise in their environment is 85dB or more.

Since decibels are on a logarithmic scale, the difference between 86dB and 98dB is large. But I searched a few aviation forums and there's very little discussion of cabin noise in light singles apart from a few subjective remarks. I couldn't find any good sources that said one aircraft type is well known as being noisier or quieter than average. The only consistent comment is that helicopters are louder than fixed-wing aircraft, which is also shown in the FAA document linked above.

Having said that, there are quite a few articles online about soundproofing aircraft in different ways. This one quotes the example of a jet:


  Aero Sound Shield is currently soundproofing a particularly large
  corporate jet - a converted McDonnell-Douglas MD-87 - for a Las Vegas
  hotel owner who is almost totally blind and who has compensated by
  developing extremely sensitive hearing. "He wants a 60-dB airplane,
  which is quieter than a Lexus," Nelson points out.


But the same article makes the point that modifying any aircraft to add soundproofing increases the weight to a point that makes the aircraft much less useful:


  Unfortunately, your airplane and mine can't accept the mass and weight
  of MD-87 measures. "I rode one time in a Piper Arrow that was very
  quiet," Nelson recalls, "but it was completely lead-lined. It could
  carry two people and half a load of fuel. That was fine for that guy,
  because that's all he ever wanted to carry, but it wasn't very
  practical."


Furthermore, it's worth remembering that modern noise-cancelling headsets are very good so the problem of noise (as opposed to vibration, which is also a factor for fatigue and health) has been more or less solved for most people. Even if you spend $1000 or more on a high-end ANR headset, that's a minor cost compared to altering the aircraft structure or materials and you still have full performance and useful load. I guess that for most GA pilots that's the decisive factor.