Here is code:
An alternative approach to not being able to use the window's sliders is to enable sliders on the dialog window, itself. These will show up automatically if you place a cap on the maximum height of the dialog but can be a little tricky with some versions of jQueryUI.
At least on the version of jQueryUI that I am on (1.9) I needed to specify the maximum height on my own because the maxHeight property that should be able to be used according to the documentation didn't work*.
Here's what worked:
$("#dialog").dialog({
modal: true,
width: "auto",
height: "auto"
/* maxHeight: whatever won't work, */
}).css("maxHeight", window.innerHeight-120);
I subtracted 120 pixels off of the window's height to accommodate for the Dialog window's header -- and footer section with its "ok" button.
* The max-height actually would take affect if the dialog was attempted to be resized -- but not upon display.