Hello,
it should be possible, just enable your search module and check its html code. There are important names of inputs. If it is dropdown box (e.g. template selection), you can also copy option value.
So finally you can add to your url something like template_area=1 to select only objects from template with id 1.
EDIT:
But if you want to have only badminton listings and tenis listings (with different templates), then you can create links in your menu (visible/hidden). JCE (Joomla Content Editor) allow you to create links in articles to existing menu items.