Did men who were trappers earn a living along the Atlantic Coast or
on the frontier?

It depended on what era of history you are talking about. Early trappers made their living in the forests that bordered the Atlantic Ocean. As the areas became more agricultural and urban game was found further west. In the post Revolutionary period, places like the Ohio Valley, Kentucky and Tennessee. In the decades after the War of 1812 and before the Civil War "Mountain Men" made their living trapping in the Rocky Mountains in the far west. It was a profession that moved west in advance of "civilization"