Our toddler, Walt, has become quite the picky eater. Veggies are clearly the enemy at this point. Two of my wife's successful techniques:
1. The "non-threatening" portion
2. The "bargaining chip"
A "non-threatening portion" is literally just 2 or 3 tiny bites. Keep it small and simple, and your child may be more willing to at least try it. And if the small portion size doesn't work, you can offer a "bargaining chip" -- if you eat just 2 or 3 bites, you can have something else that you really like.
Hope this helps!