Search module is problematic for multiple templates and there are more customers what have this problem.

I can only recommend you to use filters instead of search module. Filter works only for 1 template (actual visible object list). So customer will come to your web and select what he wants (tenis or badminton) in menu. Then he will be able to filter courts.

You can also create small menu with alias links to tenis list and badminton list. If you add this menu to column with name Search courts by, it can help your customers to find what they need.

when you create property you have couple of ticks

1.Searchable
2.Filterable
3.Object's

what is this object's?what it does i can not find it in documentation

Searchable means that property can be used in module.
Filterable means that property can be used in filter on objects list.
Objects means that property will be visible in objects list.
Object means that property will be visible in object detail.