What is the quickest and most reliable way to deal with kobolds?

+1 to Kelox for the grinder, as this is by far the most effective way to deal with both kobolds and sappers. However, because of their short range, they are not always an option, so here are a few other options:

• Tar pits. The tar pits slow kobolds down to about the speed of a normal orc, which slows them down enough for your other traps to hit them. These are especially effective with the ceiling-mace - a single ceiling-mace with tar-tiles below it will kill all kobolds and weak/medium orcs (and heavy orcs, with upgrades) if you can force them to walk along the length of the mace, leaving only trolls/ogres to deal with.
• Barricades + Grinders. If the hallway is too wide, you can force enemies to walk near the grinders using barricades. Note that this only works in a level without sappers, as sappers will destroy the barricades.
• Traps with long range will hit them when placed parallel to their movement (rather than perpendicular like usual). For instance, place arrow-traps on the wall they face just before they turn a corner.
• Archers are extremely good at taking out smaller enemies like Kobolds and Sappers. They're only useful when they can be placed far enough away that they won't be attacked. Also, be wary on levels with Gnoll Hunters, as they will go out of their way to kill your Archers.
• Kill them manually. If you are good at shooting, get a fast-shooting weapon (like the sorceress's staff, or the crossbow) and take them out yourself. And if your aim isn't so good, using the alchemist's satchel (which does splash in a large radius) can be very effective in taking out large groups of kobolds - made even more effective with tar-pits, since the kobolds will group up

The shock-zapper and brimstone will also kill them, but (as you found out) are not particularly effective at it.

I find the grinder trap to be incredibly effective at dealing with kobolds. With the unique upgrade to clear jams quicker, and one normal upgrade (for faster jam clearing), a single grinder trap was resetting it's bar to full between each kobold.

The only problem is grinders have a relatively short range, so you need to make the kobolds pass by a wall.

Dunno if anyone's tried this but I feel the Wind Belt is actually quite effective for the Sappers anyway. Upgrade the primary to increase range if you like and when you knock them back with the primary attack they just blow up when they land, killing even more Kobolds with their own explosion. It's wonderful.