This can be achieved using some javascript. With the starting point being f.ex. the bottom resizer of the control, you can implement an interval function that checks the mouse position and starts a scrolling, like this:
$resizerBottom = $('#resizableChild').find('.ui-resizable-s');
var interval;
var mousePos;
$resizerBottom.mousedown(function (e) {
mousePos = e.pageY;
$(document).mousemove(function (e) {
mousePos = e.pageY;
});
interval = setInterval(function () {
//add scroll functionality here
}, 10);
});