[MamaS]

First, try doing for them what we do for babies. They say it takes 10 presentations of a new food before a baby will eat it. Pick the food you want to start with -- say cole slaw. Call it a salad not a vegetable.
The first night, put 1 spoonful on their plate. Just one. That is all they are expected to eat. You eat a regular serving.
The next day, put 2 spoonfuls. The next day three, etc. Until you get to one-half cup. (Even I would not eat a full cup of lima beans at a meal, and I like lima beans! Let a "serving" be one-half to three-fourths cup).
Second, give them veto power. Let them choose one vegetable that they do not eat and do not have to eat. For former President Bush, it was broccoli. For me, it is beets. Tried them, don't like them, tried them several different ways, still don't like them. They grow in dirt and I can taste the dirt! Oddly, don't feel the same about potatoes, carrots or onions - they grow in dirt and I love them.