You can get plungers from many doctors, drugstores, and optical shops to help you insert and take out contact lenses. However, I won't use them because they are not sterile. If you use them improperly, it can cause damage to your eyes.
I guess there is no such device that can help you insert and take out the contact lenses automatically. But it is quite a good idea. If such device exists, it must be very popular. You can buy extended contacts which don't need to get in and take out frequently.