If your kids are older (school aged) and you have farmer's markets nearby, give them each $5 to spend (at least $3.50 must be spent on vegetables) on something they pick out that they must then be willing to try.
Then, search out recipes and cook the new vegetable together.
If your kids are little (toddler aged), then you will just have to keep offering. Generally, it takes an average of 10-12 times before a young child will even TRY a new food.
If your children will eat meatloaf or spaghetti sauce, chopped vegetables are easy to add to both items. Soup is another good way to get vegetables into them, but not the best thing now that the weather's warmer (unless you try gazpacho).
If all else fails, fresh or lightly steamed veggies with a variety of homemade dips or spreads can be a great way for kids to experiment with vegetables.
Good luck!