I've got tons of salad recipes! They're my fall-back for pot lucks.

Here are a few favorites:
1) You said no leafy greens, but if you're not opposed to broccoli and/or cauliflower, you can make a nice salad by chopping raw broccoli/cauliflower florets into bite-sized chunks and tossing with a dressing of 8 oz. Miracle Whip-type salad dressing, 2 T. sugar and 2 T. cider vinegar (you'll end up with something probably about like salad cream, I'm guessing?). I also add shredded mild cheese, crumbled, crispy bacon/pancetta, sunflower seeds and raisins, but you could add any other sweet/crunchy bits you like. Very versatile.
2)
Easy Pasta salad: Cook a 1-pound box of rotini, farfalle, or other pasta of your choice. Add whatever chopped veggies/cheese you'd like (olives, grape tomatoes, capers, feta, etc), then toss with a couple spoonfuls of any prepared pesto sauce. Depending on how strongly flavored you want it, you can cut the pesto with a drizzle of olive oil.
3) Wild Rice Salad: (I
think I got this from a Martha Stewart book)
1 1/2 t. salt
3 c. wild rice
4 blood oranges or navel oranges, peel & pith removed
3 T. red-wine vinegar
3 T. sherry vinegar
1 t. ground black pepper, plus more for seasoning
1/2 c. extra-virgin olive oil
6 scallions, white and green parts cut into 1/8-inch rounds
1 c. dried cranberries
1 bunch fresh, flat-leafed parsley, chopped
1. In a large saucepan, cook rice according to package instructions until just tender, about 40 minutes
2. Drain rice in colander
3. While rice cooks, carefully section the oranges, working over a bowl to catch the juice as well
4. In a separate bowl, combine vinegars, salt and pepper, then slowly whisk in oil
5. In a large serving bowl, combine rice, oranges, scallions, cranberries, parsley, oranges and juice
6. Drizzle vinaigrette over mixture and gently toss. Season with salt & pepper to taste.
7. Best served at room temperature