The Little Coffin Hunters were a group of young boys in the town of Hambry that idolized and, in a childish way, imitated the mercenary Big Coffin Hunters. Already known to cause borderline criminal mischief across the town, the boys were largely looked down upon and chased away by the thugs they worshiped, and warned off of using their preferred name. While it was a mild ego boost for the Bigs, it also chafed them to be stuck in one town, however prosperous, and these boys were a reminder of that.
Since Stephen King drew so much inspiration from the works of JRR Tolkien in creating the Dark Tower, it is worth noting a parallel in these boys. In Tolkien's started but quickly abandoned sequel to Lord Of The Rings, called The New Shadow, Aragorn's son and heir faces a world where the race of Men is starting to become corrupt and weaken in its resolve, with some adults worshiping the spider-demon Ungoliant, and some children play-pretending that they are Orcs. It seems possible that the Little Coffin Hunters were partly inspired by this unfinished story, where the children had already reduced the Orcs' carnage to a game, just as the Littles living in a corrupted world looked not at the Gunslingers as hero-figures, but at these vicious outlaws.