I'm not sure if you just want to be able to make the recipes, or if you also want to have the juniper taste without the allergic reaction so to speak. Finding a substitute shouldn't be too hard, but they won't quite have the same taste. Vodka is suggested for martini-type drinks:
This is a tough one to pull off, but in general, if you are making martini-type drinks, gin can sometimes be substituted for vodka, and vice versa. While these alcohols taste quite different, the texture and appearance of a cocktail is not altered by switching, and can often be just as good.
From: http://www.drinknation.com/bartending/substitute
I came across a video on making something gin-like out of vodka, but it says “juniper berries are the key ingredient.” Perhaps you could still add the cardamom and other spices to match the gin flavor more closely though. Here's another page with similar instructions (check the page for the recipe):
But what many people don’t realize is that gin and vodka begin life in the exact same way. You could even say that gin is nothing more than infused vodka. [...] In his book The Complete Guide to Spirits (HarperCollins, 2004), Anthony Dias Blue describes cold compounding as a legitimate method for producing gin.
From: http://www.jeffreymorgenthaler.com/2007/how-to-make-your-own-gin-without-a-still/
For other types of drinks, Cook's Thesaurus lists a few other possible substitutions:
gin This is distilled from grains and similar to vodka except that it's flavored with juniper berries, herbs, peels, and spices. London gin = dry gin = English gin = London dry gin is the preferred gin for martinis and other mixed drinks. American gin is similar, but isn't quite as heavy and dry as London gin. Hollands gin = sweet gin = Dutch gin = Geneva gin = Jenever is sweeter and more aromatic than other gins and isn't normally used for mixed drinks. Tanqueray and Beefeater are well-respected brands. Don't confuse gin with sloe gin, which is sweetened.
Substitutes: vodka (This turns a martini into a vodka martini, a gimlet into a vodka gimlet, a gin and tonic into a vodka and tonic, a Tom Collins into a vodka Collins, and so forth.) OR white rum OR whiskey OR tequila OR brandy (This turns an Alexander into a Brandy Alexander.)
From: http://www.foodsubs.com/Liquor.html
In the world of cocktails, the term for creating a drink with no alcohol is "virgin".
If you google "virgin mint julep", you will find recipes to try to simulate the beverage without bourbon. They employ a variety of strategies, but ginger ale, lemon juice, or lemonade seem to come up fairly frequently, alone or in combination.
Best Answer
It depends what the recipe is, but I've successfully replaced brandy with orange juice or apple juice in the past. It's not a direct replacement for the flavour, of course, but gives a similar strength of flavour, if you see what I mean.