Dawat-e-Paraguay!
On tourist visa no body is going to issue you an invitation letter from Paraguay. If at all, they may charge you a sum of 200 - 400 USD. Generally a tourist visa is given for a foreigner whose visit is for tourism purpose. The best way for you to get tourist visa is to get hostel/room booked in Paraguay and before finalizing the payment you can write via email to hotel owner and they will issue the invitation letter as per your requirement. Once you get the invitation letter, complete the booking and make payment and the hotel will be glad to receive you in Paraguay.