Standard widget content id

My widgets are each classed with .widget. The titles have .widget-title, but the content doesn’t have anything standard like .widget-content.

I want to style the content areas of all my widgets the same, but I have to make styles for all the different types of widgets.

What’s the easiest way for me to make something like this:

<li class="widget">
  <h3 class="widget-title">My Widget</h3>
  <div class="widget-content">
    Random widget type
  </div>
</li>