I've tried lots of fancy fluffy cotton wicks that just burn out. Some people have those little metal holder-thingies to keep the wick in place; some use bobby pins as holder thingies. If your oil cups are plastic, the metal holder things will melt the oil cups!
I've given up and gone to floating wicks. Any other suggestions?
Those nice old-fashioned, Genie-esque "lamp" things look great, but how do they work?!