Make a big deal of making yummy noises. Little eyes will immediately turn to you. These are sort of for big people. Make a big deal out of letting them have one. If your child genuinely does not like carrots it may not work, but if he or she does, you could be in business.
Children are much more open minded about new things when they have a hand in planning.
When you begin to peruse your vegetables for the evening meal, get their input. If you want your child to try carrot sticks or celery sticks, make them pretty. Cut their sandwich into triangles and arrange the vegetable sticks like butterfly wings. Or try giving them a small plastic bowl of their favorite dressing or dip. Stick the carrot or celery sticks in the dip like little flags.