I know they have the 737-600, but i think they could make a huge profit if they made a Small RJ like CRJ or Embraer does. I think Boeing could do really well with that. The 737-600 has not done very well!!!
Though there is no generally accepted definition of a regional jet, I agree with those who call it a jet seating 100 or less passengers. With that definition in mind, both Airbus and Boeing have aircraft that are just above that seating capacity. Airbus has the A318 with a single class seating of 117 while Boeing actually produced the recently discontinued 717-200 (106 single class seats).
I don’t think either manufacturer could produce both the larger jets and a regional jet without one affecting the other. It would require them to build new facilities because their current facilities could not handle the additional load.
There is also the matter of Embraer and Bombardier. Both have extensive experience in producing regional jets. I don’t believe Boeing or Airbus would ever be able to get a decent market share if they competed against these two companies.
Boeing did look into making a smaller version of the 717-200. This would have sat approximately 75 to 80 passengers.
As you may recall, Boeing owned deHavilland for a very short period in the 80’s. The Boeing order books are full, they don’t need the distraction. They’ve outsourced most of their production work already.
Side note: have you ever seen a Challenger, Dash8 and CRJ on a ramp next to each other? It’s kind of like seeing Michael and Latoya Jackson in the same room. They may not exactly be the same but they have a lot of the same parts and they sure look alike. See also: Beechcraft King Air 200 and Pilatus PC12.