Indigo (or, for that matter, any Indian carrier) offers billing at the airport.
Even for online registration, there are many seats available for free, which include the middle seats and those in the back of the plane. You can choose one of them and complete the check-in.
Alternatively, just go to the airline counter at the airport and you will be assigned a random seat at check-in. If you are lucky, you can get a free premium seat (window or aisle and in front of the aircraft).
Source – Personal experience with indigo.