Since technical solutions are not acceptable (on this site, on other sites they would be more than welcome), the situation is: Your neighbours want X, it seems a reasonable request to them, but from your point of view there is no way you can give them X. For reasons that are good, but that your neighbour doesn't understand. In this situation, giving them X is unacceptable, but telling them "you can't have X" will not go down well (Oleg's comment "I would definitely be offended by that").
In this case, you could try giving them the wrong password, and after half an hour trying to get it to work you give up. Or you claim that you don't know the password, your son-in-law has set up everything on the WiFi and you have no idea what the password is and no idea how to find out what the password is (my wife would have actually no idea what the WiFi password is or how to find it, so this is quite a reasonable explanation).
I don't like lying generally, especially when it is unnecessary. In this case, I feel it is the best you can do. Obviously this is a situation where you get better results with a technical solution than with an interpersonal solution, so you might check on other sites.
Concerning recent comments: Somebody hasn't read the question properly. The question was "What's the best way to decline sharing my WiFi network with neighbours". I have the impression here that some people aren't reading the question properly and are downvoting for answering it.