6” 4ohm driver for small box?

Possibly you could tell us a bit more about what type of design you want?
You don't say if you wanted ported or a sealed box, two way or full range driver?
Parts express website has suggested enclosure sizes for most of the bass mid bass drivers they sell.

Have a look at Troels Gravesen website, and other speaker designer websites, just look at their bookshelf designs. Plus magazine etc Klang and Ton. There will be many 6" that can be made to perform in that size box as it is a sensible size for manufacturers to make their drivers compatible with although many of the drivers optimised for a reflex maybe happier in a cabinet of 12 - 20 litres. Lots of box calculator programmes will help decide.
The practical answer is that most 6" bass drivers will perform well in 10-12 litres. A Hi-fi speaker has three significant variables. (1) Cabinet volume. (2) Driver. (3) Vent. In tuning, these variables are balanced to produce the desired outcome. For example, the Peerless SKO165 was a popular driver amongst many manufacturers. Toshiba would utilise the driver in a 22 litre floor-stander and claim an f3 of 48hz. Another manufacturer will install the driver in a 10 litre bookshelf speaker and declare an F3 of 50hz.

12 litres for 2hz more in lower frequency response is a Devil's bargain.
Not least, port tuning can compensate for the loss of output @48hz. But nothing (over 3dB) is for free, Boosting output @48hz has a price - it may cost you 10dB at 30hz.
The more technical members will explain the science.
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There is a peerless SLS or SDS 6inch paper cone with smaller magnet that can work sealed or vented. Have you considered a sealed box. I am guessing that some of the Visaton, or Monacor drivers identified in replacement question for older loudspeakers would fit the bill As they seem to be flexible designs

There was a nice design posted as a simple but good build during Covid, but I cant remember who posted it. That may have been along the dimensions you are seeking. I am reasonably sure it used a traditional European driver possibly the Visaton w170-8 or 170-4.