The term "coach gun" came into use because of Wells Fargo bank. In 1858, they opened a stage coach route between Tipton, Missouri and the fast growing city of San Francisco, California. Not only did they transport passengers on this route, they also transported mail for the US post office, as well as large sums of paper money and gold to their branches. The route was 2800 miles long and passed through some of the wildest parts of the United States. Naturally, this attracted the attention of bandits and highwaymen and so these stage coaches were pretty heavily guarded. The driver of the stage-coach was at a disadvantage, because he had to concentrate on driving the horses, hence they would put a person next to him with a coach gun, to defend the two of them as needed, and there were additional guards inside the stage coach as well. Since it is difficult to hit a moving target from a bouncing stage coach, which is also moving at speed, the guards preferred a coach gun to a rifle, since all one needed to do was point the gun in the general direction and pull the trigger.
The same idea was also later used in Australia, by banks seeking to transfer large sums of money across different Australian towns.
There was no specific coach gun maker, as many manufacturers were making them: Remington, Lefever, Ithaca, Sharps Arms Manufacturing, Colt, Parker etc. are some of the famous names that made them.
As you can see from the above video, they can pack a punch.
Coach guns are still being manufactured by some companies, but sale may be restricted in certain areas, due to rules about what the minimum length of a shotgun should be.