I've been researching refrigerator pickle recipes and came across this one using zucchini. 

Zucchini Refrigerator Pickles

4 cups zucchini slices, 1/8" thick
1 cup onion sliced thinly
3 cloves garlic, sliced thinly
1 cup white vinegar
1/2 sugar
3/4 teaspoon red pepper flakes
1 teaspoon mustard seeds
3/4 teaspoon salt
[list type=decimal][*]Combine vinegar, salt, sugar, mustard seeds and red pepper flakes in small saucepan and bring to a boil.  Remove from heat and stir to dissolve sugar.[*]In a large bowl, combine zucchini, onion and garlic.  Pour dressing over the vegetables and toss to coat.[*]Cover and chill in fridge for at least twenty-four hours.[/list]  
Notes: Above is the original recipe (I forget where I found it) and I hate when they give vegetable measurements in cups instead of just telling you how many of what size to use!  So, I used two medium sized zucchini, one medium onion and used a mandoline to get nice thin slices of each. 

As for the garlic, I used the already minced stuff in the jar - about one heaping teaspoon.  Instead of red pepper flakes, I used an actual sweet red pepper, large, and after removing the seeds and pithy ribs, julienned it.  Instead of sugar, I used an equal amount of Splenda.

I would recommend stirring the vegetables occasionally during the chilling process to make sure everything gets marinated nicely in the dressing.  One last thing, you can peel the zucchini before slicing it up if you prefer - I didn't bother.