in our home we don't give an alternative, its worked for us so far.
For example if I give a new food I do it at lunch, then if she wont eat I five it to her again at dinner. She has a small snack mid afternoon, by supper though she's hungry and will eat what I give her.
We believe (as my parents did) that you eat what you get, and we don't have the money to waist food to be honest. Sometimes there is no choice, what she gets is all there is. I have yet to have her go without all day.
If, on the other hand, she tries the food and really doesn't like it we will give her something else. We also know not to make that again. This way she knows that she does have some choice. So far it works great for us. DD very rarely doesn't try what we give her, and very rare does she actually not like it. DD is actually one of the least picky toddlers I know, even the daycare had been suprised at how easily she tries new foods.
We've actually done the same with her since we introduced foods. If she didn't want it at first we kept trying untill she ate it and we found 95% of the time she liked it as soon as she tried it.