Do a google search of Coton de Tulear. It is in the bichon family. They are wonderful dogs and don't shed either. A close friend of mine has one. They don't really bark- they only sort of "chirp". They are beautiful dogs and very smart too. We own a toy fox terrier and she is pretty good about barking - but not all are- and male terriers in general bark more than females. Our little girl only barks when people come to the door or she is really excited while playing. We have worked VERY hard though to mitigate barking with her and she has been trained to understand us saying "that's enough" and then she stops. It's important to remember that dogs who bark, bark for many reasons. When dogs bark at someone at the door or noises outside, they are doing what they are instinctively programmed to do- it's their job to protect and alert you. You can work on that with them though. Then there are dogs who don't get enough attention and bark because they are under stress and lonely. Hope this helps.
Another good choice that is wonderful with children and very gentle are Shelties. They are gorgeous and very loving and trainable..
Shelties are very vocal dogs. It isnt really a bark, but it is a really unique vocalization, kind of a howl/bark/yelp.
I would recommend checking out akc.org for different ideas. It gives the breed standard for personality and also how easy/hard they are to train. It's a great reference and might help you discover a breed that you didn't even think of before.
I also heard shih tzu's aren't barkers. I'm sure you can also train most dogs to not bark quiet as often.
You might want to try a havanese. They are part of the bichon family and are very trainable. Hopefully my DBF will let me get one this year! They are so adorable and very loving and playful. I read they get along very well with children. And, they aren't "shedders" so that's a big plus!
i cant believe no one mentioned a frenchie or a boston terrier! theyre the quietest breeds ive ever met, and make fabulous family dogs bc they dont tend to bond to one person in particular
^^I agree! Another one to add to the list:
<-------PUGS!!! They are the greatest, most lovable, most fun dogs ever! Mine do not bark what so ever, and on occasion when they do, it's a very soft and quiet bark. Not yippy and annoying like a terrier or something .
I also suggest the Coton de Tulear. Very, sweet, docile dogs that will alert but not yap for the heck of it. They're very athletic little dogs, so if you like to hike or do mild climbing, that's a big plus.