My son was a very picky eater. What we ended up doing is feeding him several small "snack" meals a day; something he liked that was good for him, so he would get nutrition! We would try new foods on him or take something he liked and change it a little, to expand his "likes".
He sat with the family at meals, even if he was not hungry.
We NEVER bribed him.
He is now 6 feet tall, about 210 pounds and solid as a rock (you met him a couple of times at tailgates - late 90's). He likes all kinds of food now and really likes to cook gourmet foods.
It is a phase where you want to kill him, but it will pass.