I don't have a quick fix, but a few things have helped me avoid some of the pain.
First, I make sure the tape is wet so either just out of the shower (I think the steam helps, too) or by covering it with oil of some kind. Second, I pull up a tiny bit of tape and get my finger under it. By keeping a finger on the skin and pulling little by little, I can usually lessen the pain pretty significantly.
Hope that helps!