AFAIR custom house will not sell if amount of goods is below some number (e.g. 50) or price is low (but I'm not sure that one).

Have you tried clicking on your Customs House and making sure the goods you want to sell are ticked?

Also, I don't think goods will sell if they number fewer than 50.

I could be wrong here, as it has been a while since I have played, and I usually just let my CH do its own thing. However, I think that while you can build a CH in every city, only one will sell goods each turn. It sells a maximum of 3 types, and always sells the largest quantities first.

If that is the case, then it may simply be the other cities are outperforming that particular city, thus causing it to never sell goods, or at the very least to n not sell very often.

All of them sell and as many goods "types" as you like per turn. Wont sell below 50 units. If a good is ready to sell it will appear green in warehouse.