Actually there is no eye exercise to make your eyes become bigger. But if your eyes feel comfortable, they will be at the relaxing state. The pupil may become big. Then the eyes will show big. You could do the eyes healthy exercise which may do help for your bright eyes.
Well, I quite understand your feelings , however, as far as I know, there are simply no ways to achieve this goal, since the size of our eyes are born and not to be changed in a natural way. But if you insist on doing this, I recommend that you use some eye makeups to make them appear bigger, or you might as well carefully choose a cosmetics hospital to take a surgery, but this way is not to be taken without careful thought.
As far as i could know, there is no eye exercises that can make your eyes look bigger. The size of the eyes are born with it. If you want to make it bigger, you may have to take surgery or take cosmetic way. Personally, i recommend you do it in a cosmetic way. For example, you can draw eyeliner, curl eyelashes and use mascara that can make your eyes look bigger.
Well, you should know that your eyes are the same size as when you were born and they do not get any larger. So generally speaking, you can not do exercises to make it become bigger, but you can do something to make it look bigger. There are many ways you can have arty. For example, you can put on white eyeliner on your water line or Wear fake long eyelashes. So that, it can make your eyes be bigger. Also, you can wear Circle lenses which can do a good job to your eyes too.