I've cleaned drop-in coils using pure-grain alcohol such as Everclear, moonshine, or Vodka over 100 Proof. The higher and purer the alcohol content the better, though. Let them soak overnight, repeat as necessary, then air-dry for another overnight period, and they are rejuvenated, but not quite good-as-new. This is mostly to remove flavor from wicks, but it will do a decent job cleaning the coil of crud.
Seriously though, with the coils I use being so cheap (and rebuildable), I don't even bother cleaning them anymore... I just grab another and toss the old one into the "rebuild later" pile.