You can not target a specific area with exercise. And I can't think of anything that will help with a double chin. Some people just have them, even some skinny people have them.
I could be wrong... but your best bet is just to keep working on losing weight and hope it goes away. I am sure it will in time.
I agree - a double chin is the result of excess fat, not weak muscles. The best exercise for losing a double chin is cardio: walking, running, swimming, biking, treadmill, elliptical etc. Those will burn calories and help you get rid of the fat under your chin.
I had a horrible double/triple chin to start with. (who knows it didn't stop, couldn't tell I even had a neck). The good thing was, it was one of the first places the weight loss was clearly visible. Good luck to you and I know it will be gone for you soon.
Mine was just fat, too. It disappeared somewhere around as I passed 38% bodyfat. At 35%, there's only a thin layer of fat left under my chin. Pretty soon it will be all gone, I expect.
Double Chin
I had a work out instructor at a gym give me some guidance on that subject years ago. This is what he told me to do. Stick your lower jaw out real far in front of your face. You will feel two ridges on each side of your neck. Hold for a count of 5. Do 3 sets of 5. The sagging chin sucks up when you look in a mirror. Now chew with your neck like this in an exaggerated cow fashion opening and closing your mouth as wide as you can. You will actually feel soreness when you first start this. It worked for me. The weight loss will also help.
double chin?
The best exercise for losing a double chin is cardio: walking, running, swimming, biking, treadmill, elliptical etc. Those will burn calories and help you get rid of the fat under your chin. 
