Clarins makes my eyes sting, I use Vaseline or baby oil but I tend to have bags under eyes so perhaps they are too heavy. I like oily remover if possible though.
Smurf I have very very sensitive eyes and for years I have found the only eye make remover I can use (have tried all expensive ones like Clarins etc) is Boots own brand in a small blue tub about £2 I think. Boots essentials fragrance free for all skin types eye make up remover pads (40 in tub)