M.L.
I think kids need to do their "toughening up" themselves. All you can do is encourage.
At the moment, she may feel that, in addition to being naturally sensitive (it's not unusual to be quick to cry as well as to laugh), her friends, her coach, and even her family members are now telling her she's a wimp and a loser. How is a little girl going to handle that?
You may get a lot of better answers, but I think one thing you can do is look for the times when she does things without the tears. Really be on the lookout - and commend her when that happens. "I'm glad that when you fell down you just checked to see if you were all right and then went on playing. Good for you!"
You could give her behavioral cues occasionally (and unobtrusively). "J., look on the menu, and if you don't see anything you like right away, tell me very quietly and I'll help you look."
How loud is her gymnastics coach? Does she find his yelling frightening? How can she know for sure that he's just raising his voice because that's what he does, and not being furiously angry? Eight years old is still pretty young.
With encouragement and some guidance, she will find that she can save her tears for the occasions that really call for them, and handle everything else with thought. Her happy disposition will actually help her.