Look in the frozen section at the grocery store and you will find a multitude of different veggie sides that you just heat on the stove or in the microwave. Some are already seasoned or have sauces. Some also have pasta in them as well. I prefer frozen veggies over canned anyway because they are supposed to retain more of their nutrients in the freezing process vs. the canning process. Now, I do still use some canned veggies so I'm not totally dissing those, I just find the taste and added nutrition in frozen veggies more preferable in most cases. I will state if you're more used to canned veggies, going with frozen may be a bit of a taste shock to your family 'cause it takes longer to soften some veggies up that have been frozen, like carrots and green beans, than the canned versions. But to get my family to eat the more healthy sides, I just cook them a little longer to improve the texture for them and they just gobble them right up.
Knorr has some new rice and pasta sides that have 2 servings of vegetables in each bag that you can find next to the rice and mac & cheese section of the grocery store. I can't remember the name of the side, but we have tried the chicken rice flavored one and even my picky daughter seemed to like it ok. I know it's processed, which some people would really poopoo, but when I'm busy, I'm not against using a bag or box to make dinner if you know what I mean.
I don't know if your family likes corn, but if they do, here's a good recipe from Paula Deen:
Corn Casserole
Recipe courtesy Paula Deen
Show: Paula's Home Cooking
Episode: Country Cooking - Southern Sides
1 (15 1/4-ounce) can whole kernel corn, drained
1 (14 3/4-ounce) can cream-style corn
1 (8-ounce) package corn muffin mix (recommended: Jiffy)
1 cup sour cream
1/2 cup (1 stick) butter, melted
1 to 1 1/2 cups shredded Cheddar
Preheat oven to 350 degrees F.
In a large bowl, stir together the 2 cans of corn, corn muffin mix, sour cream, and melted butter. Pour into a greased 9 by 13-inch casserole dish. Bake for 45 minutes, or until golden brown. Remove from oven and top with Cheddar. Return to oven for 5 to 10 minutes, or until cheese is melted. Let stand for at least 5 minutes and then serve warm.
This recipe is by far not a healthy dish but it's probably one of my husband's favorite.
I also recommend looking for side dish recipes on these websites: www.recipezaar.com (my favorite), www.allrecipes.com or www.foodnetwork.com. On the first two, you can even specify that you want "simple" recipes in your search.
Good luck!