Ulee grew out of his first pair of climbing shoes. They are little blue La Sportivas. They aren't marked with a size, but should fit up to like a five year old. When they are that young you can totally just get by with tennis shoes, and when he first started wearing them they were way too big, but he was psyched to put on his own climbing shoes like dad. Still plenty of use left in these things.
$15 or trade or something
The shoes are found in these pictures: