maybe cherry flavoring in the cookie batter and lime or lemon juice in the frosting? all a shirley temple is made of is sprite or 7 up and cherry...
You could add some grenadine (that's what they put in the drink at the bar) and chopped up maraschino cherries to the cookie batter and a very lightly lemon/lime royal icing, but very lightly and not too sour since that would take away from the cherry flavor.
You can usually find grenadine where they sell the margarita salts and stuff like that at the grocery store. 
Isn't grenadine made from pomegranets, not cherry? You could add some grenadine to the cookie dough in place of extract. I also wonder if you made a glace icing using 7Up in place of the milk or water if it would work? Some lemon and lime extract would probably work better, though.
Nowadays, most of the grenadine you find at the store apparently doesn't have any fruit in it at all and is just fruit flavoring on a syrup base. But yes, grenadine is tradition made from pomegranate juice.
The being said, I do think the cherry flavor would be needed in one form or another. A Shirley Temple never tastes as good without the cherry floating in it.
I'm not really sure what else to suggest that hasn't already been said. But if you play around with this, I'd love to know how it goes because this sounds really good right now.
Recipe here with ingredients for Shirley temple. Lemon lime pop, grenadine, splash of orange juice & a maraschino cherry. Also has recipe for making your own grenadine. I'd just experiment with mixing the flavors until you find it to your liking. Be great if there was an extract for each one. Be a lot easier!
http://www.canadianliving.com/food/kiddie_cocktail_shirley_temple.php
My version of a shirley temple was from the 1950's. Just gingerale and merichino ( I know I spelled that wrong sorry!) cherry with an umbrella .
possible gingerbread cookies with a frosting where you add the juice and puree a few of those cherries to get the flavour. ( I've done that to cupcakes and it is just the right taste).
I think if you put the cherry flavour in the frosting and top with a piece of cherry you will get more of a real taste. Go for a real whole cherry if you are going for the "look" as well.
I always had shirley temple's with ginger ale, too. I've made Shirley Temple cookies using a ginger cookie, iced with pomegranate/grenadine flavored icing and drizzled with cherry icing.
That's the thing though... grenadine is what they use in the drink. Some places might make their own grenadine, but the drink is made with the sickly sweet, artificially flavored grenadine syrup with a couple maraschino cherries thrown on top. I've always had them made with ginger ale too, but I think a ginger cookie would over power the whole thing and it would be all you would taste.
Traditionally it is two parts gingerale, one part orange juice, and a splash of grenadine. Most places these days make it with Sprite/7-Up and grenadine.
My brother LOVES Shirley Temples... LOL... even now at 31.
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