A search on Amazon, Best Buy, and Newegg for trackball and sorting the results from lowest to highest price all include scrolling buttons, either by touch, scroll ring, scroll wheel. The dirt cheapest option I could find for 20 bucks, the Logitech Trackman Trackball has something called WebScroll buttons and other cheap Logitech trackballs use SetPoint.
It appears, at least from all the evidence I can gather, that trackballs without a scroll option is a very rare exception and would need to be from a model older than 10 years.