The best way to do this if not the module handle it is to make a new container. A copy of one existing and add a cssclass to the content there.
Lets say you add scroll as a class.
and then in the css file add
.scroll
{
height:1000px;
overflow:auto;
}

(This could have been done in the header and footer of the module too but I think IE8 will render it wrong due to how DNN inject some classes)