Sri Lankan hospitality means that people will go to any length to please young and finicky eaters, and most places offer at least a few Western-style dishes, though child-specific menus are rare.
To average Western tastes, Sri Lankan food is spicy and you may find your little ones don’t like it. That’s fine as many places serve pancakes or omelettes and you’ll also find pasta, pizza and chips in many tourist towns. To ease children into Sri Lankan food, try a breakfast of pittu. The combination of coconut and rice will be kind to their palates. Also try hoppers (bowl-shaped pancakes), especially the string variety, or nice and mild rotti flatbreads with a filling. If all else fails, there is tropical fruit aplenty and you can always find plain rice.
Note that highchairs in restaurants are uncommon!