What thickness lancet are you using?
You might be able to get a thicker one.
I agree with
@Jim Lahey about the side of the finger - I find the side of my middle finger about parallel with the base of the nail is a good place.
If you work with your hands that can also toughen them up especially the finger tips so you should perhaps look for a soft place.
Finally I find it easier to get blood after exercise; I assume the blood is flowing and the capillaries have opened up to help keep me cool. Certainly easier after a bike ride than first thing in the morning.