The traditional rig for catching coalfish afloat is the flying collar or various versions of it. This consists of either a long, wire French Boom (shown below) or a plastic tube boom sliding on the mainline or leader, followed by a bead, and ending in a small, high-quality swivel.
The hooklength is tied to the other end of this swivel, and is usually clear monofilament of around 20-30lb between 8-12ft in length. The lure is tied to the end of this.
If using modern spinning tackle, as described, above the lure, typically, a weighted shad is tied directly to the end of the leader, dropped straight down to the bottom and wound back up through the entire water column with a steady retrieve.
When fishing for coalfish over reefs, some anglers still use strings of up to six feathers, or their various modern equivalents, such as Hokkai lures. These are fished either baited or unbaited, and can catch huge numbers of fish, but provide little in the way of sport.