I don't know dog breeds well enough by sight, and they have changed quite bit over the last few hundred years, but there are numerous portraits of people with their dogs. Here's a small article that talks a bit about it. Likely, there would have been numerous variations of spaniels and hounds. Pugs were around as well. If you can't find specific information about American breeds, the colonies would most likely have had the same dogs as the English, though I know some specific American hound breeds developed during this time.
I think you might revise your question to ask what breeds of dogs were common during the Revolution. In my studies and reading, aside from the well off city folk, dogs were used as guard dogs, hunting dogs, general farm animals rather than what we today would consider 'Pets'.
