Puncture-proof 20" tires?
If you want something that really is absolutely puncture-proof:  http://www.greentyre.co.uk/bicycle-tyres.php

But they are extremely hard work to fit and, more importantly, they combine the harsh feel of a small hard tyre with the high rolling resistance of an underinflated tyre, and they lack grip. (At least that was my experience with some 700c ones years ago; they might have improved, but I doubt it. But I was getting punctures several times a month until I fitted them. I went back to standard tyres when I changed my commute route. The Marathon Plus wasn't available then.)

Review of another similar puncture proof foam filled tyre (doesn't have a 20" size available, but gives a second opinion on the merits of such tyres): http://gearjunkie.com/flat-free-foam-bike-tires

For normal pneumatic tyres Marathon Plus is about as close to puncture proof as you can get. They can be quite stiff to get on and off though (nothing like as bad as the GreenTyres though).

http://www.londoncyclist.co.uk/why-do-boris-bikes-hardly-ever-get-punctures/

There are other 20" tyres with a puncture resistant belt, the Primo Comet for example, or the Panaracer Minit Lite "PT Shield", or the Marathon Supreme (lighter than the Plus), but I don't know of anything else as resistant as the Plus.

It won't really protect against pinch flats though. Either teach your friend to check her tyre pressure and use a pump, or do it for her.