Simple way, use the sitewide bottom widget area then add the rules below in Main Options > Fonts & Custom > Custom CSS Rule box
#sitewide-bottom-widget-area {display:none;}
.archive #sitewide-bottom-widget-area {display:block;}
Cons with that method is that the area is always loaded just not shown on non archive pages.
To avoid loading it, you could instead use he Dynamic Widgets plugin , and use Dynamic widgets to only show the widgets you put in there on archive pages